Systems Biology: Biological Networks, Network Motifs, Switches and Oscillators

Systems Biology: Biological Networks, Network Motifs, Switches and Oscillators



From Biological switches and clocks

The living cell receives signals from its environment and its own internal state, processes the information, and initiates appropriate responses in terms of changes in gene expression, cell movement, and cell growth or death. Like a digital computer, information processing within cells is carried out by a complex network of switches and oscillators, but instead of being fabricated from silicon transistors and quartz crystals, the cell’s computer is an evolved network of interacting genes and proteins. In the same way that computer design was made possible by a sophisticated theory of electronic circuitry, a basic understanding of cellular regulatory mechanisms will require a relevant theory of biomolecular circuitry. Although the ‘engineering mindset’ is sorely needed to make sense of the cell’s circuitry, the squishy, sloppy, massively parallel, analogue nature of biochemistry is so different from the solid-state, precise, sequential, digital nature of computers that the mathematical tools and intellectual biases of the solid-state physicist/electrical engineer are not entirely appropriate to unravelling the molecular logic of cell physiology. New modelling paradigms and software tools are evolving to meet the challenges of the new ‘systems biology’ of the living cell.



System Biology includes study of the following among other areas.

  • Biological Networks
  • Network Motifs
  • Switches
  • Oscillators



Biological Networks

  • Protein–protein interaction networks
  • Gene regulatory networks (DNA–protein interaction networks)
  • Gene co-expression networks (transcript–transcript association networks)
  • Metabolic networks
  • Signaling networks
  • Neuronal networks
  • Between-species interaction networks
  • Within-species interaction networks


Network Motifs:

  • Coherent Feedforward Loop (FFL)
  • Incoherent Feedforward Loop
  • Feedback Loop
  • Scaffold Motifs
  • Bi Fan
  • Multi Input Motifs (MIM)
  • Regulator Chains
  • Bi-Parallel
  • Single Input Module (SIM)
  • Dense Overlapping Regulon (DOR)


Biological Switches

  • Ultrasensitivity
  • Switches (Bistability)


Biological Oscillators

  • Clocks
  • Negative Feedback Only Oscillators
    • Repressilator
    • Pentilator
    • Goodwin Oscillator
    • Frazilator
    • Metabolator
  • Negative + Positive Feedback Oscillators
    • Meyer and Strayer model of Calcium Oscillations
    • van der Pol Oscillator
    • Fitzhugh-Nagumo Oscillator
    • Cyanobacteria Circadian Oscillator
  • Negative + Negative Feedback Oscillator
  • Negative and Positive + Negative Feedback cell cycle Oscillator
  • Fussenegger Oscillators
  • Smolen Oscillator
  • Amplified Negative Feedback Oscillators
  • Variable link Oscillators


Synthetic Biology study design of networks, switches, and oscillators.


From The dynamics and robustness of Network Motifs in transcription networks

Network Motifs

Even though biological systems are extremely complex, some of its complexity could be simplified. The study of a complex system in its entirety could prove impossible with current theories and technology. However, mathematical modelling has sought to distil the essence of complexity into concepts readily understandable by today’s science. One of such approaches has been reported by means of the study of pathways of interaction of biological networks. By concentrating on similar features that biological networks share, it has been recently discovered that at a cellular level, regulation and transcription Networks display certain patterns of connectivity at a much higher rate than expected in an equivalent randomized network. These recurring patterns of interaction, or network “Motifs”, can help us define bread classes of networks and their types of functional elements. In the same way, they can reveal the evolutionary aim by which they have been developed. Network Motifs can be interpreted as structures that have emerged as direct a reflection of the constraints under which the network has evolved. These network Motifs have been found in the biological networks of many systems, suggesting that they are the building blocks of transcription networks [4]. It has been suggested that in biological networks, these recurrent Network Motifs are responsible for carrying out key information processing tasks in the organism [5].


From Coupling oscillations and switches in genetic networks.

Switches (bistability) and oscillations (limit cycle) are omnipresent in biological networks. Synthetic genetic networks producing bistability and oscillations have been designed and constructed experimentally. However, in real biological systems, regulatory circuits are usually interconnected and the dynamics of those complex networks is often richer than the dynamics of simple modules. Here we couple the genetic Toggle switch and the Repressilator, two prototypic systems exhibiting bistability and oscillations, respectively. We study two types of coupling. In the first type, the bistable switch is under the control of the oscillator. Numerical simulation of this system allows us to determine the conditions under which a periodic switch between the two stable steady states of the Toggle switch occurs. In addition we show how birhythmicity characterized by the coexistence of two stable small-amplitude limit cycles, can easily be obtained in the system. In the second type of coupling, the oscillator is placed under the control of the Toggleswitch. Numerical simulation of this system shows that this construction could for example be exploited to generate a permanent transition from a stable steady state to self-sustained oscillations (and vice versa) after a transient external perturbation. Those results thus describe qualitative dynamical behaviors that can be generated through the coupling of two simple network modules. These results differ from the dynamical properties resulting from interlocked feedback loops systems in which a given variable is involved at the same time in both positive and negative feedbacks. Finally the models described here may be of interest in synthetic biology, as they give hints on how the coupling should be designed to get the required properties.


From Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops

To test the generality of the idea that positive feedback enables an oscillator to have a tunable frequency and constant amplitude, we examined several other oscillator models, including five negative feedback–only models: (i) the Goodwin oscillator, a well-studied model relevant to circadian oscillations (18, 19); (ii) the Repressilator, a transcriptional triple-negative feedback loop constructed in Escherichia coli (20); (iii) the “Pentilator,” a Repressilator with five (rather than three) repressors; (iv) the Metabolator (21), a synthetic metabolic oscillator; and (v) the Frzilator, amodel of the control of gliding motions in myxobacteria (22). In four of the cases (Goodwin, Repressilator, Pentilator, and Metabolator), the amplitude/frequency curves were inverted U-shaped curves similar to that seen for the negative feedback–only cell cycle model (Figs. 1B and 3A). In the case of the Frzilator, the legs of the curve were truncated; the oscillator had a nonzero minimal amplitude (Fig. 3A). For all five of the negative feedback–only models, the oscillators functioned over only a narrow range of frequencies (Fig. 3A).

We also examined four positive-plus-negative feedback oscillators: (i) the van der Pol oscillator, inspired by studies of vacuum tubes (12); (ii) the Fitzhugh-Nagumo model of propagating action potentials (23, 24); (iii) the Meyer-Stryer model of calcium oscillations (25); and (iv) a model of circadian oscillations in the cyanobacterial KaiA/B/C system (26–28). In each case, we obtained a flat, wide amplitude/frequency curve (Fig. 3B). Thus, a tunable frequency plus constant amplitude can be obtained from many different positive-plusnegative feedback models; this feature is not peculiar to one particular topology or parameterization.

These findings rationalize why the positiveplus- negative feedback design might have been selected through evolution in cases where a tunable frequency and constant amplitude are important, such as heartbeats and cell cycles. However, it is not clear that an adjustable frequency would be advantageous for circadian oscillations, because frequency is fixed at one cycle per day. Nevertheless, the cyanobacterial circadian oscillator appears to rely on positive feedback (26), and positive feedback loops have been postulated for other circadian oscillators as well (Table 1). This raises the question of whether the positiveplus- negative feedback design might offer additional advantages.

One possibility is that the positive-plusnegative feedback design permits oscillations over a wider range of enzyme concentrations and kinetic constant values, making the oscillator easier to evolve and more robust to variations in its imperfect components. We tested this idea through a Monte Carlo approach.We formulated three simple oscillatormodels: (i) a three-variable triple negative feedback loop with no additional feedback (Fig. 4A), (ii) one with added positive feedback (Fig. 4B), or (iii) one with added negative feedback (Fig. 4C). We generated random parameter sets for the models and then for each set determined whether the model produced limit cycle oscillations.We continued generating parameter sets until we had amassed 500 that gave oscillations.


From Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops




Key Terms:

  • Ultra-sensitivity
  • Bi-stability
  • Positive Feedback Loop
  • Negative Feedback Loop
  • Biological Oscillators
  • Biological Switches
  • Biological Networks
  • Network Motifs
  • Regulation Networks
  • Signalling Networks
  • Communication Networks
  • Biological Clocks
  • Circadian Rhythms
  • Harmonic Oscillators
  • Van der Pol Oscillator (Limit Cycle)
  • FitzHugh–Nagumo oscillators (Neural)
  • Limit Cycle Oscillator
  • Cell Cycle
  • Systems Biology
  • Synthetic Biology
  • Gene Regulatory Networks
  • Kuramoto Oscillators
  • Phase Coupled Oscillators
  • Cardic Pacemaker
  • Biochemical Networks
  • Synchronization
  • Goodwin Oscillator
  • Repressilators
  • Fussenegger Oscillators
  • Smolen Oscillators
  • Variable Link Oscillators
  • Metabolators
  • Amplified Negative Feedback Oscillators




Key Sources of Research:



Ultrasensitivity Part I: Michaelian responses and zero-order ultrasensitivity

James E. Ferrell Jr. and Sang Hoon Ha

Click to access nihms-629459.pdf





Ultrasensitivity Part II: Multisite phosphorylation, stoichiometric inhibitors, and positive feedback

James E. Ferrell Jr. and Sang Hoon Ha


Click to access nihms686079.pdf




Ultrasensitivity part III: cascades, bistable switches, and oscillators

James E. Ferrell Jr and Sang Hoon Ha


Click to access nihms635216.pdf




Robust Network Topologies for Generating Switch-Like Cellular Responses

Najaf A. Shah1, Casim A. Sarkar

Click to access pcbi.1002085.pdf





Feedback Loops Shape Cellular Signals in Space and Time

Onn Brandman1 and Tobias Meyer


Click to access nihms101299.pdf




Interlinked Fast and Slow Positive Feedback Loops Drive Reliable Cell Decisions

Onn Brandman, James E. Ferrell Jr, Rong Li2,3,4, and Tobias Meyer

Click to access nihms180881.pdf




Positive feedback in cellular control systems

Alexander Y. Mitrophanov and Eduardo A. Groisman

Click to access nihms-58057.pdf




Effect of positive feedback loops on the robustness of oscillations in the network of cyclin-dependent kinases driving the mammalian cell cycle

Claude Gerard, Didier Gonze and Albert Goldbeter



Design Principles of Biochemical Oscillators

Béla Novak and John J. Tyson




Design principles underlying circadian clocks

D. A. Rand1,†, B. V. Shulgin1, D. Salazar1,2 and A. J. Millar




Positive Feedback Promotes Oscillations in Negative Feedback Loops

Bharath Ananthasubramaniam*, Hanspeter Herzel




Efficient Switches in Biology and Computer Science

Luca Cardelli1,2, Rosa D. Hernansaiz-Ballesteros3, Neil Dalchau1, Attila Csika ́sz-Nagy

Click to access pcbi.1005100.pdf




Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops

Tony Yu-Chen Tsai,1* Yoon Sup Choi,1,2* Wenzhe Ma,3,4 Joseph R. Pomerening,5 Chao Tang,3,4 James E. Ferrell Jr




Biological switches and clocks

John J. Tyson1,*, Reka Albert2, Albert Goldbeter3, Peter Ruoff4 and Jill Sibl


Click to access 2008_Tyson_J_R_Soc_Interface.pdf




Network thinking in ecology and evolution

Stephen R. Proulx1, Daniel E.L. Promislow2 and Patrick C. Phillips


Click to access 65601ed2a5c67143b6d4be7193c02235a279.pdf




Networks in ecology

Jordi Bascompte


Click to access Bascompte%202007.pdf




Network structure and the biology of populations

Robert M. May


Click to access may.pdf




Biological networks: Motifs and modules


Click to access BMIF310_network_B_Motifs_2009.pdf




Analysis of Biological Networks: Network Motifs


Click to access lec04.pdf




Regulatory networks & Functional motifs

Didier Gonze


Click to access network_motifs.pdf




Structure and function of the feed-forward loop network motif

S. Mangan and U. Alon


Click to access 11980.full.pdf




Network Motifs: Simple Building Blocks of Complex Networks

R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, U. Alon


Click to access MiloAlon2002.pdf




The dynamics and robustness of Network Motifs in transcription networks

Arturo Araujo

Click to access Network_Motifs.pdf




Formation of Regulatory Patterns During Signal Propagation in a Mammalian Cellular Network

Avi Ma’ayan, Sherry L. Jenkins, Susana Neves, Anthony Hasseldine, Elizabeth Grace, Benjamin Dubin-Thaler, Narat J. Eungdamrong, Gehzi Weng, Prahlad T. Ram, J. Jeremy Rice, Aaron Kershenbaum, Gustavo A. Stolovitzky, Robert D. Blitzer, and Ravi Iyengar


Click to access nihms266526.pdf




Toward Predictive Models of Mammalian Cells

Avi Ma’ayan, Robert D. Blitzer, and Ravi Iyengar

Click to access nihms266522.pdf




Modeling Cell Signaling Networks

Narat J. Eungdamrong and Ravi Iyengar

Click to access nihms453834.pdf




Bistability in Biochemical Signaling Models

Eric A. Sobie

Click to access nihms-332970.pdf



An Introduction to Dynamical Systems

Eric A. Sobie


Click to access nihms-332968.pdf




Computational approaches for modeling regulatory cellular networks

Narat J. Eungdamrong and Ravi Iyengar

Click to access nihms-453838.pdf



Systems Biology—Biomedical Modeling

Eric A. Sobie,* Young-Seon Lee, Sherry L. Jenkins, and Ravi Iyengar




Network analyses in systems pharmacology


Seth I. Berger and Ravi Iyengar

Click to access btp465.pdf



Biological Networks: The Tinkerer as an Engineer

U Alon


Click to access Biological%20Networks%20The%20Tinkerer%20as%20an%20Engineer.pdf



Cell Biology: Networks, Regulation and Pathways



Click to access tkacik+bialek_09b.pdf




Coupling oscillations and switches in genetic networks

Didier Gonze


Click to access d29052b34bc3fe43649c826fd9fd0506e445.pdf




Biological Oscillators and Switches


Click to access Murray-Math-Biol-ch7.pdf




Design principles of biological oscillators


Didier Gonze

 Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos


Irving R. Epstein

Kenneth Showalter



Modelling biological oscillations


Shan He


A comparative analysis of synthetic genetic oscillators


Oliver Purcell1,*, Nigel J. Savery3, Claire S. Grierson4 and Mario di Bernardo2,5


Hierarchy Theory in Biology, Ecology and Evolution

Hierarchy Theory in Biology, Ecology and Evolution


I have always been intrigued by multi-level thinking whether it is in organizations, biology, ecology, and evolutionary theory.

  • Plant – Division – Corporate – Industry – Macro-economy
  • Molecules – Organelles – Cells – Tissue – Organs – Whole body
  • Organism – Populations – Communities – Ecosystem –  Bio-Sphere


How does human body forms from Molecules?  Is it all evolutionary?  or is there a role for Vitalism?

How to integrate decision making in organizations at multi levels?  From Corporate level to Plant Level.

How does an Individual fits in Groups, Communities, Society, and Ecosystem?

What is the role of fractals thinking in Evolutionary Biology?



The Hierarchy theory is a dialect of general systems theory. It has emerged as part of a movement toward a general science of complexity. Rooted in the work of economist, Herbert Simon, chemist, Ilya Prigogine, and psychologist, Jean Piaget, hierarchy theory focuses upon levels of organization and issues of scale. There is significant emphasis upon the observer in the system.

Hierarchies occur in social systems, biological structures, and in the biological taxonomies. Since scholars and laypersons use hierarchy and hierarchical concepts commonly, it would seem reasonable to have a theory of hierarchies. Hierarchy theory uses a relatively small set of principles to keep track of the complex structure and a behavior of systems with multiple levels. A set of definitions and principles follows immediately:

Hierarchy: in mathematical terms, it is a partially ordered set. In less austere terms, a hierarchy is a collection of parts with ordered asymmetric relationships inside a whole. That is to say, upper levels are above lower levels, and the relationship upwards is asymmetric with the relationships downwards.

Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.

Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.

Level of observation: this type of level fits into its hierarchy by virtue of relative scaling considerations. For example, the host of a skin parasite represents the context for the population of parasites; it is a landscape, even though the host may be seen as belonging to a level of organization, organism, that is lower than the collection of parasites, a population.

The criterion for observation: when a system is observed, there are two separate considerations. One is the spatiotemporal scale at which the observations are made. The other is the criterion for observation, which defines the system in the foreground away from all the rest in the background. The criterion for observation uses the types of parts and their relationships to each other to characterize the system in the foreground. If criteria for observation are linked together in an asymmetric fashion, then the criteria lead to levels of organization. Otherwise, criteria for observation merely generate isolated classes.

The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply. Upper levels are above lower levels by virtue of: 1) being the context of, 2) offering constraint to, 3) behaving more slowly at a lower frequency than, 4) being populated by entities with greater integrity and higher bond strength than, and 5), containing and being made of – lower levels.

Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.

Duality in hierarchies: the dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole. Arthur Koestler in his “Ghost in The Machine” referred to the notion of holon, which means an entity in a hierarchy that is at once a whole and at the same time a part. Thus a holon at once operates as a quasi-autonomous whole that integrates its parts, while working to integrate itself into an upper level purpose or role. The lower level answers the question “How?” and the upper level answers the question, “So what?”

Constraint versus possibilities: when one looks at a system there are two separate reasons behind what one sees. First, it is not possible to see something if the parts of the system cannot do what is required of them to achieve the arrangement in the whole. These are the limits of physical possibility. The limits of possibility come from lower levels in the hierarchy. The second entirely separate reason for what one sees is to do with what is allowed by the upper level constraints. An example here would be that mammals have five digits. There is no physical reason for mammals having five digits on their hands and feet, because it comes not from physical limits, but from the constraints of having a mammal heritage. Any number of the digits is possible within the physical limits, but in mammals only five digits are allowed by the biological constraints. Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility. Forget the distinction, and biology becomes pointlessly confused, impossibly complicated chemistry, while chemistry becomes unwieldy physics.

Complexity and self-simplification: Howard Pattee has identified that as a system becomes more elaborately hierarchical its behavior becomes simple. The reason is that, with the emergence of intermediate levels, the lowest level entities become constrained to be far from equilibrium. As a result, the lowest level entities lose degrees of freedom and are held against the upper level constraint to give constant behavior. Deep hierarchical structure indicates elaborate organization, and deep hierarchies are often considered as complex systems by virtue of hierarchical depth.

Complexity versus complicatedness: a hierarchical structure with a large number of lowest level entities, but with simple organization, offers a low flat hierarchy that is complicated rather than complex. The behavior of structurally complicated systems is behaviorally elaborate and so complicated, whereas the behavior of deep hierarchically complex systems is simple.

Hierarchy theory is as much as anything a theory of observation. It has been significantly operationalized in ecology, but has been applied relatively infrequently outside that science. There is a negative reaction to hierarchy theory in the social sciences, by virtue of implications of rigid autocratic systems or authority. When applied in a more general fashion, even liberal and non-authoritarian systems can be described effectively in hierarchical terms. There is a politically correct set of labels that avoid the word hierarchy, but they unnecessarily introduce jargon into a field that has enough special vocabulary as it is.


This bibliography is in chronological order, so that the reader can identify the early classics as opposed to the later refinements. If you must choose just one book to read, turn to the last reference in this bibliography, Ahl and Allen, 1996. Simon, H.. A. 1962. The architecture of complexity. Proceedings of the American philosophical society 106: 467-82. This is the foundation paper of hierarchy theory originating from an economist. It was a re-published in “Sciences of the Artificial” by Simon. It introduces the idea of near-decomposability. If systems were completely decomposable, then there would be no emergent whole, because the parts would exist only separately. The “near” in near-decomposable allows the upper level to emerge from the fact that the parts anre not completely separate.

Koestler, Arthur. 1967. The ghost in the machine. Macmillan, New York. This is a long hard look at human social structure in hierarchical terms. The notion of holon first occurs in this work. This is a classic work, but is easily accessible to the lay public.

Whyte, L.. L.., A. G. Wilson and D. Wilson (eds.). 1969. Hierarchical structures. American Elsevier, New York. This is a classic collection of early scholarly works by some of the founders of hierarchical thinking.

Pattee, H.. H. (ed.) 1973. Hierarchy theory: the challenge or complex systems. Braziller, New York. This edited volume has some classic articles by Pattee, Simon and others.

Allen, T. F. H. and T. B. Starr. 1982. Hierarchy: perspectives for ecological complexity. University Chicago Press. This book has a significant ecological component but is much more generally about hierarchical structure. It is abstract and a somewhat technical treatment but has been the foundation work for the application of hierarchy theory in ecology and complex systems theory at large.

Salthe, S. 1985. Evolving Hierarchical Systems: their structure and representation. Columbia University Press, New York. This book has a strong structural bias, in contrast to the process oriented approach of Allen and the other ecologists in this bibliography. Salthe introduces the notion of the Triadic, where there is a focus on 1) the system as both a whole above the levels below and 2) a part belonging to another level above, 3) not forgetting the level of the structure itself in between. While much biological hierarchy theory takes an anti-realist point view, or is at least reality-agnostic, wherein the ultimate reality of hierarchical arrangement is left moot, Salthe’s version of hierarchy theory is concerned with the ultimate reality of structure. The anti-realist view of structure is that it is imposed by the observer, and may or may not correspond to any ultimate reality. If structure does correspond to ultimate, external reality, we could never know that to be so. Salthe’s logic is consistent but always takes a structural and ontological position.

O’Neill, R. V., D. DeAngelis, J. Waide and T. F. H. Allen. 1986. A hierarchical concept of ecosystems. Princeton University Press. This is a distinctly ecological application of hierarchy theory, making the critical distinction between process functional ecosystem approaches as opposed to population and community relationships. It is an application of hierarchy theory to ecosystem analysis.

Allen T. F. H. and T. Hoekstra. 1992. Toward a unified ecology. Columbia University Press. This book turns on hierarchy theory, but is principally a book about ecology. It goes beyond the O’Neill et al book, in that it makes the distinction between many types of ecology (landscape, ecosystem, community, organism, population, and biomes) on the one hand, and scale of ecology on the other hand. It ends with practical applications of hierarchy theory and ecological management.

Ahl, V. and T. F. H. Allen. 1996. Hierarchy theory, a vision, vocabulary and epistemology. Columbia University Press. This slim a volume is an interdisciplinary account of a hierarchy theory, and represents the shallow end of the pool. It is the primer version of Allen and Starr 1982. It is full of graphical images to ease the reader into a hierarchical perspective. It makes the distinction between levels of organization and levels of observation. It takes a moderate anti-realist point of view, wherein there may be an external reality, but it is not relevant to the discourse. We only have access to experience, which must of necessity involve observer values and subjectivity. There are examples from a wide discussion of many disciplines. Included are examples from psychology, ecology, the law, political systems and philosophy. It makes reference to the global and technological problems facing humanity, and offers hierarchy theory as one tool in the struggle. The summary of hierarchy theory in the opening paragraphs above comes from this book.

This summary was compiled by

Timothy F. Allen, Professor of Botany,
University of Wisconsin Madison,
Madison Wisconsin 53706 — 1381.
Email –



Key People:

  • James Grier Miller
  • Howard Pattee
  • Stanley Salthe
  • T F Allen
  • Herbert Simon
  • CS Holling



Key Sources of Research:



T Allen



Hierarchy Theory

Paweł Leśniewski


Click to access 2006-06-28_-_Hierarchy_Theory.pdf



Summary of the Principles of Hierarchy Theory

S.N. Salthe


Click to access Summary_of_the_Principles_o.pdf





Jon Umerez


Click to access umerez.pdf




Hierarchy Theory as the Formal Basis of Evolutionary Theory


Click to access HierarchyTheoryastheFormalBasisofEvolutionaryTheory.pdf



The Concept of Levels of Organization in the Biological Sciences


PhD Thesis Submitted August 2014 Revised June 2015

Daniel Stephen Brooks



A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications

Jianguo Wu , John L. David


Click to access Wu_David_2002.PDF



What is the Hierarchy Theory of Evolution?


Click to access What-Is-The-Hierarchy-Theory.pdf




Jackson R. Webster


Click to access 274.pdf



Ecological hierarchies and self-organisation – Pattern analysis, modelling and process integration across scales

Hauke Reutera,, Fred Jopp, José M. Blanco-Morenod, Christian Damgaarde, Yiannis Matsinosf, Donald L. DeAngelis


Click to access Reuter_etal_BAAE%202010.pdf



Levels of organization in biology: on the nature and nomenclature of ecology’s fourth level

William Z. Lidicker, Jr


Click to access Artigo4.pdf



Chapter 24

Hierarchy Theory: An Overview

Jianguo Wu




Recent progress in systems ecology

Sven E. Jørgensena, Søren Nors Nielsenb, Brian D. Fath

Click to access 55f1782708ae199d47c2624c.pdf


Click to access Jorgensen%20et%20al%202016.pdf



Heterarchies: Reconciling Networks and Hierarchies

Graeme S. Cumming



Evolutionary Theory





Holons, creaons, genons, environs, in hierarchy theory: Where we have gone

Timothy Allen, Mario Giampietro



The Evolutionary Foundations of Hierarchy: Status, Dominance, Prestige, and Leadership

Mark van Vugt & Joshua M. Tybur

Click to access Handbook_of_Evolutionary_Psychologymvv2014rev.pdf



The Microfoundations of Macroeconomics: An Evolutionary Perspective

Jeroen C.J.M. van den Bergh

John M. Gowdy


Click to access 00021.pdf



Understanding the complexity of Economic, Ecological, and Social Systems

C S Holling

Click to access Holling_Complexity-EconEcol-SocialSys_2001.pdf



Hierarchical Structures

Stanley N. Salthe


Click to access 5768411408ae7f0756a2248c.pdf



Two Frameworks for Complexity Generation in Biological Systems

Stanley N. Salthe


Click to access A-life_Conf_paper_Word.pdf

Click to access _publ_classified_by_topic.pdf



Spatial scaling in ecology



Click to access Spatial%20scaling%20in%20ecology%20v3%20n4.pdf



The Spirit of Evolution

by Roger Walsh

An overview of Ken Wilber’s book Sex, Ecology, Spirituality: The Spirit of Evolution (Shambhala, 1995).

Bank of Finland’s Payment And Settlement System Simulator (BoF-PSS2)

Bank of Finland’s Payment And Settlement System Simulator (BoF-PSS2)


From Payment and Settlement System Simulator


The Bank of Finland provides a simulator called BoF-PSS2 for replicating payment and securities settlement systems. The simulator is adaptable for modelling multisystem setups that can be a combination of payment, securities settlement systems and CCP’s. The simulator is known to be unique and the first of its kind. Since its launch in 2002 it has been distributed to more than 90 countries and has contributed to numerous studies and research papers.

The simulator can be used to fulfill some of the regulatory requirements stated in the PFMI’s and BCBS requirements such as identifying the liquidity risks inpayment systems. Here under are topics the simulator can be used for:

  • Settlement, liquidity and credit risks in FMI’s
  • Systemic Risks and Counterparty risks in FMI’s
  • Identification of critical counterparts
  • Policy change impact evaluation
  • Network analysis
  • Liquidity dependency analysis
  • Relationship analysis of Monetary policy and liquidity needs for settlement of payments
  • Evaluation of sufficiency of liquidity buffers and margins
  • System merger effects on liquidity needs
  • System performance benchmarking
  • Netting algorithm testing and development
  • System development and prototyping

In comparison to static calculations of indicators, the simulation results naturally incorporate network (or systemic) effects rising from the payments flows and the technical properties of the infrastructures themselves. The results obtained from simulations are directly interpretable and have a self-evident meaning which is not always the case with all indicators. The results can directly be used for risk management purposes for example when evaluating the sufficiency of liquidity buffers and margins. Computer simulations take advantage of using the available information in full without losing micro-level information due to indicator aggregations.

The simulator is freely available for research purposes, and has already been introduced in numerous countries. It is possible to tailor and adapt the simulator to specific payment systems. Several adaptations of the simulator have already been made, eg. for TARGET2. The simulator team provides trainings, consultation and tailored adaptations which are priced for cost recovery. The training course aims at providing necessary skills for efficient use of BoF-PSS2 with hands on computer class exercises. It also presents numerous examples from real studies where the tool has been used. For more details see the training course outline. Minimum attendance to the session is four participants.

Basically, trainings are organised upon demand and it is also possible to order a training course to be held onsite outside the proposed dates.


From Payment and Settlement System Simulator / Product Page


From Payment and Settlement System Simulator / Documentation page

The Bank of Finland Payment and Settlement System Simulator, version 2 (BoF-PSS2), is a powerful tool for payment and securities settlement system simulations. The simulator supports multiple system structures and various settlement models.

The simulator is designed for analysing liquidity needs and risks in payment and settlement systems. Special situations, often difficult or impossible to test in a real environment, can be readily simulated with BoF-PSS2. Thus, users can study how behavioral patterns and changes in policy and conventions impact the payment and settlement systems and participants. The efficiency of gridlock-resolution and liquidity-saving measures can be analyzed as well.

The application is divided into three sub-systems:

  • Input sub-system for preparing and defining the input data,
  • Execution sub-system for running simulations,
  • Output sub-system for basic analyses of simulation results.

Different settlement logics are implemented into separate algorithms. To replicate specific systems, appropriate algorithms must be selected with appropriate parameters. Different algorithm combinations can be used to replicate a large number of current and potential settlement conventions and structures. Real-time gross settlement systems (RTGS), continuous net settlement systems (CNS), deferred net settlement systems (DNS) and hybrid systems can be implemented with the simulator as well as securities settlement and multicurrency systems. Inter-system connections and bridges make it possible to define multi- system environments consisting of various types of interdependent systems. E.g. it is possible to replicate the interaction of RTGS and securities settlement systems.

Advanced users of BoF-PSS2 can define and build their own user modules/algorithms and expand the basic features of the simulator to analyse new types of settlement processes. It is also possible to implement agent based modeling by adding algorithms replicating the participants’ behavior and decision making to control and alter the flow of submitted transactions. As a later addition, the simulator also has a network analysis module for generating networks and network indicators from either input data or results of simulations.

BoF-PSS2 has an easy to use graphical user interface. It is also possible to automate the use of the simulator via its command line interface (CLI).


From Payment and Settlement System Simulator / Product Page


A separate TARGET2 simulator version of BoF-PSS2 has been developed and delivered for the European System of Central Banks. It is based on the same basic software architechture and features of BoF-PSS2. Additional features are implemented as separate algorithm modules which replicate the proprietary algorithms of actual TARGET2 system. It is used by Eurosystem for quantitative analyses and numerical simulations of TARGET2.

TARGET2 simulator has been jointly delivered by Suomen Pankki (Bank of Finland) and the 3CB (Banca d’Italia, Deutsche Bundesbank, Banque de France) based on a decision of ECB Governing Council.



Key Terms

  • Liquidity Simulator
  • Payment System
  • Risk Management
  • Financial Stability
  • Cascades of Failures
  • Congestions and Delays
  • Financial Market Infrastructures
  • Payment Networks
  • Contagion
  • RTGS
  • Simulation Analysis
  • Intraday Payments


Key People

  • Harry Leinonen
  • Tatu Laine
  • Matti Hellqvist
  • Kimmo Soramäki



Key Sources of Research:


Payment and Settlement System Simulator – A tool for analysis of liquidity, risk and efficiency

Bank of Finland Payment and Settlement Simulator



Click to access 2006_11a_hl.pdf



BoF-PSS2 Technical structure and simulation features

Harry Leinonen

Click to access 20031519seminarpresentationleinonen2.pdf



Payment and Settlement System Simulator






Quantitative analysis of financial market infrastructures: further perspectives on financial stability




Diagnostics for the financial markets : computational studies of payment system : Simulator Seminar Proceedings 2009-2011




Simulation analyses and stress testing of payment networks




Simulation studies of liquidity needs, risks and efficiency in payment networks : Proceedings from the Bank of Finland Payment and Settlement System Seminars 2005-2006




Liquidity, risks and speed in payment and settlement systems : a simulation approach




Simulation Analysis and Tools for the Oversight of Payment Systems


Click to access 2012-12-vigilanciasistemasdepago-10.pdf



Utilizing the BoF simulator in quantitative FMI analysis

Tatu Laine

Banco de México



Click to access %7B15D9D1D3-D455-1E98-6FA6-AFB3B30C4ACB%7D.pdf



TARGET2 Simulator

Click to access target_newsletter_7_2013.pdf



Intraday patterns and timing of TARGET2 interbank payments

Marco Massarenti

Silvio Petriconi

Johannes Lindner


Click to access 0b5a0eb557b478843891449221c6ed2e7502.pdf



Communities and driver nodes in the TARGET2 payment system

Marco Galbiatiy, Lucian Stanciu-Vizeteuz

June 17, 2015


Click to access 5593d39c08ae1e9cb42a1904.pdf



Payment Delays and Contagion

Ben Craig† Dilyara Salakhova‡ Martin Saldias§

November 14, 2014

Click to access CraigSalakhovaSaldias_2014_preview.pdf



Federal Reserve Bank of New York Economic Policy Review

September 2008 Volume 14 Number 2

Special Issue: The Economics of Payments


Click to access EPRvol14n2.pdf



Contagion in Payment and Settlement Systems


Matti Hellqvist



Click to access mh.pdf



Applications of BoF-PSS2 simulator and how to use it in agent based models


Click to access Hellqvist(presentation)_ABM-BaF09.pdf



Simulation and Analysis of Cascading Failure in Critical Infrastructure

Robert Glass, Walt Beyeler, Kimmo Soramäki, MortenBech and Jeffrey Arnold

Sandia National Laboratories, European Central Bank,  Federal Reserve Bank of New York

Click to access 07-glass_pres.pdf



Simulation analysis of payment systems


Kimmo Soramäki


Click to access 2011-11-vigilancia-07.pdf



Simulating interbank payment and securities settlement mechanisms with the BoF-PSS2 simulator

Harry Leinonen

Kimmo Soramäki




Click to access bof_dp_2303.pdf


On Anticipation: Going Beyond Forecasts and Scenarios

On Anticipation: Going Beyond Forecasts and Scenarios


From Anticipation.Info of Mihai Nadin

A Second Cartesian Revolution

For about 400 years, humankind, or at least the western world, has let itself be guided by the foundation set by Descartes and Newton. The cause-and-effect, deterministic model of the machine became so powerful that every thing and every being came to be considered a machine. As a description of the material world and as an expression of the laws governing its functioning, deterministic-based physics and Cartesian reductionism (of the whole to its parts) proved to be extremely powerful instruments in the overall progress of humankind. But neither Descartes nor Newton, nor most of their followers, could have envisioned the spectacular development of science in its current depth and breadth.

The physicist Erwin Schrödinger concluded that organisms are subject to “a new physics,” which he did not produce, but rather viewed as necessary. This new physics might well be the domain of anticipation. Indeed, from within physics itself—that is, quantum mechanics—a possible understanding of some aspects of anticipation can be derived.

The realization that the world is the unity of reaction and anticipation is not new. What is new is the awareness of the limits of our understanding a dynamics of change that transcends the deterministic view. The urgent need for such an understanding is probably best expressed in the spectacular development of the life sciences.

The perspective of the world that anticipation opens justifies the descriptor “a second Cartesian Revolution.” Instead of explaining complexity away, we will have to integrate it into our existence as the informational substratum of rich forms through which anticipatory processes take place.


From Anticipation.Info of Mihai Nadin

Anticipation: Why is it a subject of research?

Anticipation occurs in all spheres of life. It complements the physics of reaction with the pro-active quality of the living. Nature evolves in a continuous anticipatory fashion targeted at survival. The dynamics of stem cells demonstrate this mechanism. Through entailment from a basic stem cell an infinite variety of biological expression becomes possible.

Sometimes we humans are aware of anticipation, as when we plan. Often, we are not aware of it, as when processesembedded in our body and mind take place before we realize their finality. In tennis, for example, the return of a professional serve can be successful only through anticipatory mechanisms. A conscious reaction takes too long to process. Anticipation is the engine driving the stock market. Creativity in art and design are fired by anticipation.

“The end is where we start from,” T. S. Eliot once wrote. Before the archer draws his bow, his mind has already hit the target. Motivation mechanisms in learning, the arts, and all types of research are dominated by the underlying principle that a future state—the result—controls present action, aimed at success. The entire subject of prevention entails anticipatory mechanisms.


From Anticipation.Info of Mihai Nadin

Research into anticipation revealed various aspects that suggested a number of definitions.

Robert Rosen, Mihai Nadin, Daniel Dennett and others who approached particular aspects of anticipation contributed to some of these definitions. Mihai Nadin (cf. Anticipation – A Spooky Computation) attempted an overview of the various angles from which anticipation can be approached if the focus is on computation. This overview is continued and expanded in the integrated publication (book+dvd+website) to which this website belongs. The following 12 definitions, or descriptions, of anticipation should be understood as working hypotheses. It is hoped and expected that the knowledge community of those interested in anticipation will eventually refine these definitions and suggest new ones in order to facilitate a better understanding of what anticipation is and its importance for the survival of living systems.

  • An anticipatory system is a system whose current state is determined by a future state. “The cause lies in the future,”. (cf. Robert Rosen, Heinz von Foerster)
  • Anticipation is the generation of a multitude of dynamic models of human actions and the resolution of their conflict. (cf. Mihai Nadin)
  • An anticipatory system is a system containing a predictive model of itself and/or of its environment that allows it to change state at an instant in accord with the model’s predictions pertaining to a later instant. (cf. Robert Rosen)
  • Anticipation is a process of co-relation among factors pertaining to the present, past and future of a system. (cf. Mihai Nadin)
  • Anticipation is an expression of the connectedness of the world, in particular of quantum non-locality. (cf. Mihai Nadin)
  • Anticipation is the expression of natural entailment. (cf. Robert Rosen)
  • Anticipation is a mechanism of synchronization and integration. (cf. Mihai Nadin)
  • Anticipation is an attractor within dynamic systems. (cf. Mihai Nadin)
  • Anticipation is a recursive process described through the functioning of a mechanism whose past, present, and future states allow it to evolve from an initial to a final state that is implicitly embedded in the mechanism. (cf. Mihai Nadin)
  • Anticipation is a realization within the domain of possibilities. (cf. Mihai Nadin)
  • Anticipatory mechanisms can be reinforced through feedback. Feedforward and inverse kinetics are part of the integrated mechanism of anticipation. (cf. Daniel Dennett, Daniel Wolpert, Nadin)
  • Anticipation is a power law-based long-range interaction. (cf. Mihai Nadin)


From An Introduction to the Ontology of Anticipation

Recent years have witnessed the growth of significant interest in theories and methodologies which seek to foresee the future development of relevant situations. Studies of the future fall under many different denominations, and they employ a huge variety of techniques, ranging from forecasting to simulation, from planning to trend extrapolation, from future studies and scenarios to anticipatory systems. Widely different conceptualisations and formalisations have been proposed as well.1 This remarkable variety may be partly simplified by making explicit the main underlying assumptions of at least some of them. Two of these assumptions are that (1) the future is at least partly governed by the past, and (2) the future can be better confronted by opening our minds and learning to consider different viewpoints. According to (1) the future is part of a structured story whose past and present are at least partially known. The claim is defended that the forces that have shaped past and present situations will still be valid while the situation under consideration unfolds. The core thesis is that the future is embedded in the past; it is the projection of the past through the present. Time series analysis, trend extrapolation, and forecasting pertain to this family. Any of the mentioned methodologies may be further supplemented by computer-based simulations. On the other hand, instead of directly addressing the problem of searching for the seeds of the future in the past, (2) considers the different problem of preparing for the unforeseeable novelties awaiting us in the future. Learning about widely different outcomes is now the issue: one must be ready to consider and address possibly unfamiliar or alien scenarios. The main outcome of this exercise is an increased capacity to distinguish among possible, probable, and preferred future scenarios. These activities come under the heading of future studies, while scenario construction is the best known methodology adopted by practitioners. For now on I shall refer to (1) and (2) as respectively the forecasting and the scenario viewpoints. Forecasts and scenarios are not contradictory one to the other. They may and usually do coexist, since they address the future from two different standpoints. Furthermore, experience shows that both are useful. This paper introduces a third, different viewpoint, here termed the viewpoint of anticipatory systems, which can be profitably synthesized with forecasts and scenarios; i.e. it is not contradictory with the claims of either the forecasting or scenario viewpoint. Recent years have witnessed the growth of significant interest in anticipation.2 Anticipatory theories have been proposed in fields as different as physics, biology, physiology, neurobiology, psychology, sociology, economy, political science, computer science and philosophy. Unfortunately, no systematic comparison among the different viewpoints has so far been developed. It is therefore fair to claim that currently no general theory of anticipation is available. Generally speaking, anticipation concerns the capacity exhibited by some systems to tune their behaviour according to a model of the future evolution of the environment in which they are embedded. Generally speaking, the thesis is defended that “An anticipatory system is a system containing a predictive model of itself and/or its enviroment, which allows it to change state at an instant in accord with the model‟s predictions pertaining to a later instant” (Rosen [19: 341]). The main difference between forecasting and scenarios on the one hand, and anticipation on the 1 See, among many others, Adam [1], Bell [4], Cornish [5], Godet [7], Lindgren and Bandhold [8], Retzbach [16], Slaughter [22], Woodgate and Pethrick [23]. 2 Starting from the seminal Rosen [19]. See also [20], [21]. 2 other, is that the latter is a property of the system, intrinsic to its functioning, while the former are cognitive strategies that a system A develops in order to understand the future of some other system B (of which A may or may not be a component element).



Key Terms

  • Hyper Sets
  • Hyper Incursion
  • Hyper Recursion
  • Recursion
  • Incursion
  • Anticipatory Systems
  • Weak Anticipation
  • Strong Anticipation


Key People

  • Roberto Poli
  • Mihai Nadin
  • Riel Miller
  • Robert Rosen
  • John J Kineman
  • Daniel M Dubois
  • John Collier
  • Loet Leydesdorff



Key Sources of Research:


Systems and models with anticipation in physics and its applications

A Makarenko



Anticipatory Viable Systems

Maurice Yolles

Daniel Dubois

Click to access 92666ab431a3f68df0ce8139d594aaeb3f87.pdf



Anticipatory Kaldor-Kalecki Model of Business Cycle

Daniel M. Dubois


Click to access emcsr2004_Daniel-Dubois.pdf



An Introduction to the Ontology of Anticipation

Roberto Poli


Click to access read_Poli-An-Introduction-to-the-Ontology-of-Anticipation.pdf



Towards an anticipatory view of design

Theodore Zamenopoulos and Katerina Alexiou


Click to access anticipation.pdf



The role of anticipation in cognition

Alexander Riegler

Click to access Riegler%20A.%20(2001)%20The%20role%20of%20anticipation%20in%20cognition.pdf

Click to access 7d5ded82973e081a572c79bd76f8188b0ed5.pdf



SDA: System Dynamics Simulation of Inter Regional Risk Management

Using a Multi-Layered Model with Delays and Anticipation

Daniel M Dubois1, Stig C Holmberg



Click to access P1374.pdf



Anticipatory Modeling and Simulation for Inter Regional Security

Daniel M. Dubois, Viveca Asproth, Stig C. Holmberg

Ulrica Löfstedt, and Lena-Maria Öberg


Click to access dubois-C-EMCSR-2012.pdf



Attentional and Semantic Anticipations in Recurrent Neural Networks

Frédéric Lavigne1 and Sylvain Denis


Click to access lavigne-denis-2001.pdf



Not Everything We Know We Learned

Mihai Nadin



Anticipation in the Constructivist Theory of Cognition

Ernst von Glasersfeld



The Communication of Meaning in Anticipatory Systems: A Simulation Study of the Dynamics of Intentionality in Social Interactions

Loet Leydesdorff

Click to access 0911.1448.pdf



Information Systems and the Theory of Categories: Is Every Model an Anticipatory System?

M. A. Heather, B. N. Rossiter


Click to access Rossiter_Information%20systems%20and%20the%20theory%20of%20categories.pdf



Anticipation.Info of Mihai Nadin



Institute for Research in Anticipatory Systems



Robert Rosen’s anticipatory systems

A.H. Louie


Click to access 09e4150cdd961e4a87000000.pdf



Computing Anticipatory Systems with Incursion and Hyperincursion

Daniel M. DUBOIS

Click to access 559558fe08ae99aa62c720f3.pdf



Anticipatory Systems: Philosphical Methematical and Methodological Foundations.

Rosen R.

Springer; 2014.




Judith Rosen



The Many Aspects of Anticipation

Roberto Poli

University of Trento

Click to access 9b480ac8cd96999f281892caba100baacc79.pdf



Being Without Existing: The Futures Community at a Turning Point? A Comment on Jay Ogilvy’s “Facing the Fold”

By Riel Miller

Click to access Being-without-existing-The-futures-community-at-a-turning-point-A-comment-on-Jay-Ogilvys-Facing-the-fold.pdf




Roberto Poli

Balkan Journal of Philosophy. 2009;1(1):19-29.



The Discipline of Anticipation: Exploring Key Issues

Riel Miller, Roberto Poli and Pierre Rossel


Clock of the Long Now: Time and Responsibility

Clock of the Long Now: Time and Responsibility


Stewart Brand is one of my Hero.  I admire his work and have deep respect for him.

Check out his books:

  • The Media Lab
  • Whole Earth Discipline
  • How Buildings Learn
  • Clock of the Long Now

Stewart Brand and his associates are building a 10000 yr clock in west Texas.  Project is funded by Jeff Bezos.  Danny Hillis is one of the designer of the clock.  Prototypes of clock are in display in Museums in UK and here in USA.

Stewart Brand work is about promoting long term thinking—Very Long Term Thinking.  What we call long term in our day to day conversation is just Now a days in context of Long Term Thinking being promoted by Stewart Brand.

Long Now thinking would be considered equal to thinking associated with climate cycles time scales such as Milankovitch Cycles.

You can check out current status of the clock and other projects of the Long Now Foundation at its website.

  • How should Humans live and behave in context of Long Term Thinking?
  • How should the information, knowledge, culture, artifacts, languages, species, ecology be preserved?
  • What kind of world are we creating for future generations?
  • What should be preserved?
  • How should it be preserved?
  • How would people after 10000 years extract information contained in preserved objects?

These are big and deep questions?  We need philosophers like Stewart Brand to guide us.

I am ready to learn from him and other visionaries like him.


Time Horizon – Short to Very Long Term

  • Now – 3 Days
  • Now a days – 30 years
  • Long Now – 20000 years


Types of Cycles – slow moving to fast moving

  • Nature
  • Culture
  • Governance
  • Infrastructure
  • Commerce
  • Fashion


Image of Long Now Time





Key Sources of Researches:


Whole Earth comes into focus

To understand how our planet uses energy, we must integrate genetic data from microbial studies with satellite views of our planet.


Stewart Brand


Click to access 859231b770b7370c630252e3d04867fa6b9a.pdf



An Architecture of the Whole

University of California, Davis


Click to access arc-of-life-Sadler-.pdf






Click to access Carpenter_SR_MA.pdf



A Talk with Stewart Brand



The Clock in the Mountain




How to Make a Clock Run for 10,000 Years





Danny Hillis, Rob Seaman, Steve Allen, and Jon Giorgini


Click to access 1112.3004.pdf



Stewart Brand: The Long Now




The Long Now Foundation



There’s a Massive 10,000 Year Clock Being Built in a West Texas Mountain



Socio-Cybernetics and Constructivist Approaches

Socio-Cybernetics and Constructivist Approaches

There are two related concepts.

  • Socio-Cybernetics
  • Constructivist Approaches

Will appeal to people interested in Philosophy, Cybernetics, and Systems Theory.

A. Socio Cybernetics

Socio-cybernetics can be defined as “Systems Science in Sociology and Other Social Sciences” – systems science, because sociocybernetics is not limited to theory but includes application, empirical research, methodology, axiology (i.e., ethics and value research), and epistemology. In general use, “systems theory” and “cybernetics” are frequently interchangeable or appear in combination. Hence, they can be considered as synonyms, although the two terms come from different traditions and are not used uniformly in different languages and national traditions. Sociocybernetics includes both what are called first order cybernetics and second order cybernetics. Cybernetics, according to Wiener´s original definition, is the science of “control and communication in the animal and the machine”. Heinz von Foerster went on to distinguish a first order cybernetics, “the study of observed systems”, and a second order cybernetics, “the study of observing systems”. Second order cybernetics is explicitly based on a constructivist epistemology and is concerned with issues of self-reference, paying particular attention to the observer-dependence of knowledge, including scientific theories. In the interdisciplinary and holistic spirit of systems science, although sociology is clearly at the centre of interest of sociocybernetics, the other social sciences, such as psychology, anthropology, political science, economics, are addressed as well, with emphases depending on the particular research question to be dealt with.


SOCIOCYBERNETICS traces its intellectual roots to the rise of a panoply of new approaches to scientific inquiry beginning in the 1940’s. These included General System Theory, cybernetics and information theory, game theory and automata, net, set, graph and compartment theories, and decision and queuing theory conceived as strategies in one way or another appropriate to the study of organized complexity. Although today the Research Committee casts a wide net in terms of appropriate subject matters, pertinent theoretical frameworks and applicable methodologies, the range of approaches deployed by scholars associated with RC51 reflect the maturation of these developments. Here we find, again, GST and first- and second-order cybernetics; in addition, there is widespread sensitivity to the issues raised by “complexity studies,” especially in work conceptualizing systems as self-organizing, autocatalytic or autopoietic. “System theory”, in the form given it by Niklas Luhmann, and world-systems analysis are also prominently represented within the ranks of RC51. The institutionalization of sociocybernetic approaches in what was to become RC51, the Re-search Committee on Sociocybernetics of the International Sociological Association, began in 1980 with the founding of an ISA Ad Hoc Group and proceeded with the organization of ses-sions at succeeding quadrennial World Congresses of Sociology. The eventual RC51 became a Thematic Group and then a Working Group. Finally, in recognition of its extraordinary success (growing from some 30 members in early 1995 to 240 in 1998), the group was promoted to the status of Research Committee at the 1998 World Congress of Sociology in Montreal. Over these past two decades, sociocybernetics has attracted a broad range of scholars whose departmental affiliations represent the entire spectrum of the disciplines, from the humanities and the social sciences through the sciences, mathematics and engineering. Furthermore, the many countries of origin of these RC51 members attest to the wide international appeal of sociocybernetic approaches. Within this highly diverse community, there is wide agreement on some very general issues, for instance, on developing strategies for the study of human reality that avoid reification, are cognizant of the pitfalls of reductionism and dualism, and generally eschew linear or homeostatic models. Not surprisingly, however, there are also wide divergences in subject matter, theoretical frameworks and methodological practices. Many have argued that models developed for the study of complexity can be usefully appropriated for the study of human reality. Moreover, however, the emphasis in complexity studies on contingency, context-dependency, multiple, overlapping temporal and spatial frameworks, and deterministic but unpredictable systems displaying an arrow-of-time suggest that the dividing line between the sciences and the historical social sciences is fuzzier than many might like to think. What is more, in the humanities, the uniquely modern concepts of original object and autonomous human creator have come under serious attack. The coincidence of these two phenomena substantiate the impression that across the disciplines there may be observed a new concern for spatial-temporal wholes constituted at once of relational structures and the phenomenological time of their reproduction and change. In this context of rich history and exciting possibilities, the Research Committee on Sociocybernetics of the International Sociological Association extends an open invitation through the Journal of Sociocybernetics to all engaged in the common quest to explain and understand social reality holistically and self-reflexively without forsaking a concern for human values–human values not construed simply as a matter of individual ethics, but conceived as an integral part of a social science for our time.



B. Constructivist Foundations

Constructivist Foundations (CF) is an international peer-reviewed e-journal focusing on the multidisciplinary study of the philosophical and scientific foundations and applications of constructivism and related disciplines. The journal promotes interdisciplinary discussion and cooperation among researchers and theorists working in a great number of diverse fields such as artificial intelligence, cognitive science, biology, neuroscience, psychology, educational research, linguistics, communication science, sociology, mathematics, computer science, and philosophy.

Constructivist approaches covered in the journal include the theory of autopoietic systems, enactivism, radical constructivism, second-order cybernetics, neurophenomenology, constructionism, and non-dualizing philosophy.


Constructivist Approaches

Constructivist approaches support the idea that mental structures such as cognition and perception are actively built by one’s mind rather than passively acquired. However, constructivist approaches vary in function of how much influence they attribute to constructions.

Many assume a dualistic relationship between reality and constructed elements. They maintain that constructed mental structures gradually adapt to the structures of the real world (e.g., Piaget). In this view perception is the pickup of information controlled by the mental structure that is constructed from earlier perceptions (e.g., Neisser). This leads to the claim that mental structures are about learning sensorimotor contingencies (e.g., O’Regan).

Others seek to avoid the dualistic position. Either they skeptically reject that the structures of the real world can be compared with mental ones, independently of the senses through which the mental structures were constructed in the first place (e.g., von Glasersfeld), or they embrace a phenomenological perspective that considers perception as the grouping of experiential complexes (e.g., Mach).

All these approaches emphasize the primacy of the cognitive system (e.g., Llinás) and its organizational closure (e.g., von Foerster, Maturana). Hence, perceived patterns and regularities may be regarded as invariants of inborn cognitive operators (e.g., Diettrich).

Constructivist approaches can be said to differ also with respect to whether constructs are considered to populate the rational-linguistic (e.g., von Glasersfeld, Schmidt) or the biological-bodily (“enactivist/embodied” theories, e.g., Varela).


Common Denominators of Constructivist Approaches

The common denominators of constructivist approaches can be summarized as follows.

  • Constructivist approaches question the Cartesian separation between the objective world and subjective experience;
  • Consequently, they demand the inclusion of the observer in scientific explanations;
  • Representationalism is rejected; knowledge is a system-related cognitive process rather than a mapping of an objective world onto subjective cognitive structures;
  • According to constructivist approaches, it is futile to claim that knowledge approaches reality; reality is brought forth by the subject rather than passively received;
  • Constructivist approaches entertain an agnostic relationship with reality, which is considered beyond our cognitive horizon; any reference to it should be refrained from;
  • Therefore, the focus of research moves from the world that consists of matter to the world that consists of what matters;
  • Constructivist approaches focus on self-referential and organizationally closed systems; such systems strive for control over their inputs rather than their outputs;
  • With regard to scientific explanations, constructivist approaches favor a process-oriented approach rather than a substance-based perspective, e.g. living systems are defined by the processes whereby they constitute and maintain their own organization;
  • Constructivist approaches emphasize the “individual as personal scientist” approach; sociality is defined as accommodation within the framework of social interaction;
  • Finally, constructivist approaches ask for an open and less dogmatic approach to science in order to generate the flexibility that is needed to cope with today’s scientific frontiers.


Key People:

  • Felix Geyer
  • Ernst Von Glasersfeld
  • H Maturana
  • F Varela
  • Heinz Von  Foerster
  • Niklas Luhmann



Key Sources of Research:


Constructivist Foundations (CF)

Click to access riegler2005editorial.pdf

Click to access denominator.pdf



The role of sociocybernetics in understanding world futures 

Bernard Scott

Click to access 1794.pdf




Bernd R. Hornung


Click to access hornung.pdf





Click to access JoS6-2-2008.pdf

Click to access JoS7-2-2009.pdf








Felix Geyer and Johannes van der Zouwen





Growth and Form in Nature: Power Laws and Fractals

Growth and Form in Nature: Power Laws and Fractals


There are several instances of power laws found in nature and in society.  Some of the well known ones are:

  • City Sizes (Zipf’s Law)
  • Firm Sizes
  • Stock Market Movements
  • Income and Wealth (Pareto’s Law)
  • Metabolic Rate and Body Mass (Kleiber’s Law-3/4 or Rubner’s Law-2/3)


Power laws and Scaling in Biology

After 1997 paper by West et all, many publications have analyzed  empirical evidence as to what the correct exponent is and what is the fundamental theoretical basis for power law.

West found 3/4 as exponent, others have reported 1/4, 2/3, 4/5 etc.

Animals and Mammals follow 3/4 exponent.  Plants follow 2/3.

The Metabolic Theory of Ecology

Scaling in biology has a rich and important history. Typically body mass, or some other parameter relating to organism size, is related to anatomical, physiological, and ecological parameters across species. Quite remarkably, diverse organisms, from tiny microbes to the earth’s largest organisms are found to fall along a common slope, with a high degree of variance explained. The beauty of such scaling ‘‘laws’’ has been the generality in biotic organization that they suggest, and the challenge (for ecologists) has often been interpreting their mechanistic bases and ecological consequences.

Scaling laws have thus far inspired scientists in at least three major areas. First, scaling laws may illuminate biology that is otherwise shrouded. For example, if scaling relationships can account for variation in a parameter of interest, the residual variation may be much more easily examined because the major influence of some trait, say, body size, is removed. Second, some scientists have taken an interest in ‘‘the exponent’’—essentially the exponential scaling values that produce the allometric relationship. What are the precise values of these exponents? Are they all from a family of particular values (quarter powers) for many different biological relationships? This area seeks to define the generality of patterns in nature and to explore the empirical robustness of the relationships. Third, from a mechanistic perspective, if scaling laws are mechanistic and truly general, then this suggests some underlying common biological process that forms the structure and function of species and ultimately generates biological diversity. The mechanistics of scaling from metabolism and the currently favored fractal network model of resource acquisition and allocation may allow scientists to understand the laws of how life diversified and is constrained. Perhaps more importantly, such a mechanistic understanding should allow the successful prediction of evolutionary trends, responses of organisms to global change, and other basic and applied biological problems.

The Ecological Society of America’s MacArthur Award winner, James H. Brown, working together with colleagues for over a decade on scaling in biology, has arrived at an outline for a metabolic theory of ecology—a proposal for a unifying theory employing one of the most fundamental aspects of biology, metabolism. This metabolic theory incorporates body size, temperature (metabolic kinetics described by the Boltzmann factor), and resource ratios of the essential elements of life (stoichiometry). Indeed, this bold and visionary proposal is likely to inspire ecologists and provoke much discussion. My goal in assembling this Forum was to work toward a balanced discussion of the power and logic of the metabolic theory of ecology. I have asked both junior and senior scientists to evaluate the ideas presented in the metabolic theory and to go beyond the listing of strong and weak points. As such, this collection of commentaries should be viewed neither as a celebration of the theory nor as a roast of Jim Brown. It should, however, serve as a springboard for future research and refinements of the metabolic theory.

Several themes and axes of admiration and agitation emerge from the forum. The focus on metabolism, and metabolic rate in particular, is an advance that most agree is the fundamental basis for the processes of acquisition of resources from the environment and, ultimately, survival and reproduction of organisms. The combination of size, temperature, and nutrients has compelling predictive power in explaining life-history traits, population parameters, and even broader-scale ecosystem processes. The key point here is that Brown et al. are making a direct link between factors that affect the functioning of individuals and the complex role that those individuals play in communities and ecosystems. Although what we have before us is a proposal for a unified theory of ‘‘biological processing of energy and materials’’ in ecosystems, Brown et al. embrace the unexplained variation and acknowledge other areas of ecology that may not be subject to metabolic laws.

The commentaries presented in this Forum are unanimous in their admiration of Brown et al.’s broad theoretical proposal and its clear predictions. Yet, points of discussion abound and range widely: What really is the correct exponent? Does the scale at which scaling is applied affect its explanatory power? Are the laws really based on mechanism or phenomena? How does the addition of temperature and resource limitation enhance the power of scaling relationships? And, is scaling up from the metabolic rate and body mass of organisms to population dynamics, community structure, and ecosystem processes possible? This Forum ends with Brown’s response to the commentaries. Although there will be continued debate over the correct exponent, the data at hand from the broadest taxonomic groups support quarter powers. There is general agreement over the issue of scale and the fact that, depending on the scale of interest, metabolic theory may have more or less to offer. Finally, nutrient stoichiometry is the most recent addition to metabolic theory, and all agree that further research and refinement will determine the role for such nutrient ratios in the ecological scaling. The benefits of a metabolic theory of ecology are clear. The authors of this Forum have outlined some of the future challenges, and tomorrow’s questions will evaluate these theses.


Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include:

(1) life history attributes, including development rate, mortality rate, age at maturity, life span, and population growth rate;

(2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity;

(3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics.

Data compiled from the ecological literature strongly support the theoretical predictions. Eventually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.



Key Terms

  • Power Laws
  • Multi-scale
  • Fractals
  • Allometric Scaling Laws
  • Kleiber Law
  • Metabolic Ecology
  • Zipf Distribution
  • allometry
  • biogeochemical cycles
  • body size
  • development
  • ecological interactions
  • ecological theory
  • metabolism
  • population growth
  • production
  • stoichiometry
  • temperature
  • trophic dynamics




Key Sources of Research:


The Origin of Universal Scaling Laws in Biology

Geoffrey B. West


Click to access gbwscl99.pdf



Life’s Universal Scaling Laws

Geoffrey B. West and James H. Brown


Click to access Life’sUniversalScalingLaws.pdf



A General Model for the Origin of Allometric Scaling Laws in Biology

Geoffrey B. West, James H. Brown, Brian J. Enquist


Click to access West_Brown_Enquist_1997.pdf



Power Laws in Economics: An Introduction

Xavier Gabaix


Click to access pl-jep.pdf




The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization

Geoffrey B. West, James H. Brown

Click to access 1575.full.pdf




A general model for ontogenetic growth

Geoffrey B. West, James H. Brown & Brian J. Enquist


Click to access OntogeneticGrowth.pdf




Plants on a different scale

Lars O. Hedin


Click to access nature_news_views_06.pdf




The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms

Geoffrey B. West, James H. Brown, Brian J. Enquist


Click to access S1999_West.pdf








Click to access Brown_JH_MA.pdf




Complexity and Transdisciplinarity; Science for the 21st Century(?)!



Click to access Geoffrey%20West.pdf




Scaling Laws in Complex Systems


Click to access ma_scaling_laws.pdf




A General Model for the Origin of Allometric Scaling Laws in Biology

Geoffrey B. West, James H. Brown,* Brian J. Enquist

Click to access Science-1997-West.pdf




Effects of Size and Temperature on Metabolic Rate

James F. Gillooly,1* James H. Brown,1,2 Geoffrey B. West,2,3 Van M. Savage,2,3 Eric L. Charnov




Growth, innovation, scaling, and the pace of life in cities

Luís M. A. Bettencourt, Jose ́ Lobo, Dirk Helbing, Christian Kuhnert, and Geoffrey B. West


Click to access zpq7301.pdf




Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities

Lu ́ıs M. A. Bettencourt1,2*, Jose ́ Lobo3, Deborah Strumsky4, Geoffrey B. West1,2

Click to access pone.0013541.pdf





Francisco J. Martínez


Click to access Francisco-Martinez_Urban-dynamic-laws.pdf




Allometric Scaling Laws and the Derivation of the Scaling Exponent

Marcel Grunert


Click to access grunert.pdf



Cities, Markets, and Growth: The Emergence of Zipf’s Law

Jeremiah Dittmar

August 10, 2011


Click to access Zipf_Dittmar.pdf



Self-similarity and power laws


Click to access komulainen.pdf



The fractal nature of nature: power laws, ecological complexity and biodiversity

James H. Brown1,2*, Vijay K. Gupta3, Bai-Lian Li1, Bruce T. Milne1, Carla Restrepo1 and Geoffrey B. West


Click to access Fractal-Nature.pdf



Metabolic Rate and Kleiber’s Law



Patterns in Nature



Zipf, Power-laws, and Pareto – a ranking tutorial

Lada A. Adamic



The Power of Power Laws



Re-examination of the 3/4-law of Metabolism



Click to access Dodds%20et%20al%202001.pdf



Fifth dimension of life and the 4/5 allometric scaling law for human brain

Ji-Huan He, Juan Zhang


Click to access he2004a.pdf



Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Hai-Tao LI1*, Xing-Guo HAN2 and Jian-Guo WU


Click to access W020090624623546294020.pdf



Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant?



Click to access FE.pdf



Evidence against universal metabolic allometry.

Folmer Bokma


Click to access bokma2003u.pdf



An evaluation of two controversial metabolic theories of ecology


Click to access Louw2011.pdf




Karl J. Niklas1, and Sean T. Hammond



􏱂􏱅Network Allometry

Click to access network%20allometry.pdf



A critical understanding of the fractal model of metabolic scaling

José Guilherme Chaui-Berlinck


Click to access 3045.full.pdf




Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals

Geoffrey B. West*†‡, William H. Woodruff*§, and James H. Brown

􏰻􏰽􏱃􏱄􏱁􏱂􏰾 􏰼􏰿􏰿􏱁􏱀􏰽􏱃􏱂􏱅
􏱝􏱏 􏱨􏰼􏱂􏱹􏱃􏰼􏱻􏱍􏱑 􏱫􏱏 􏱫􏱹􏱷􏱁􏱻􏱍􏱒 􏱦􏱏􏱞􏱏 􏱞􏰼􏱻􏰼􏲀􏰼􏱂􏱍􏱓 􏱝􏱏 􏱫

Shapes and Patterns in Nature

Shapes and Patterns in Nature


There are so many colors, shapes, and patterns in nature.

  • Seashells
  • Animal Skins (Zebra, Leopard)
  • Butterflies
  • Shape of Plants
  • Flowers (Sun Flower)
  • Fruits (Pineapple)

How do we explain these from perspective of science?  There are several branches of science which have explored these questions for decades.  There are Reaction Diffusion Models and Cellular Automata models explaining development of patterns on seashells, plants and animal skins.  There is L-system developed by Aristid Lindenmayer to explain development of plants.  It is a fascinating subject.


From Exploring Complex Forms in Nature Through Mathematical Modeling: A Case on Turritella Terebra

There are several studies have been carried out in a number of scientific disciplines, such as mathematics, biology, paleontology and computer engineering to understand and decipher the relations of the seashells complex forms. Starting with Descartes, Figure 4 shows a time line in which many investigators having focused on the curves of these shells and their mathematical properties. They all outlined a number of mathematical relations that control the overall geometry of seashells.

After examining the existing seashell models in literature it is seen that they all followed Raup’s model which roughly abstracts the seashell form using three parameters; whorl (rate of expansion of the generating curve), distance (relative distance between the generating curve and axis of coiling), and translation (the change of the cone’s movement along an axis with respect to the whorl), an ellipse as the whorl cross-section as well. However, it is clear from the observations of actual shells (Figure 5) that the cross-section is more complex than the input that the three parameters allow. In the pursuit of realistic visualizations, Kawaguchi enhanced the appearance of shell models using filled polygons which represented the surface of shells more convincingly than line drawings. Similar techniques were used subsequently by Oppenheimer (1986). A different approach was adopted by Pickover (1989) who approximated shell surfaces by using interpenetrating spheres. Illert (1989) introduced Frenet Frames (Bronsvoort, 1985) to precisely orient the opening of a shell. His model also captured a form of surface sculpture. Cortie (1989) studied the pattern forms on the surface of the shell model (Meinhardt, 2003). Finally, the model of seashell geometry by Fowler et al. (2003) was similar to that introduced by Raup, and was the first to implement free-form cross sections using a Bézier curve (Farin, 2002 Rogers, 2001) as the input. It can be claimed that, studies above all focused on modeling the appearance of the shell surface.

All these approaches can be considered as a milestone for their era, as each model reflects the observation and tools of measurement, modeling and technologies of their time. In all these approaches seashells were modeled as a single surface, as a twodimensional object, and embedded in three-dimensional space. Today, such modeling research should be carried out employing observation tools, knowledge, information, and computational technologies to the maximum extent. For this reason, we developed a mathematical model that can be transformed into a computational model for further studies (such as overall behavior of shells, form-structure relations, form finding explorations etc.) to explore potentials of such optimized forms.


From Exploring Complex Forms in Nature Through Mathematical Modeling: A Case on Turritella Terebra




From Computational models of plant development and form

A broad program of using mathematical reasoning in the study of the development and form of living organisms was initiated almost 100 yr ago by D’Arcy Thompson (1942) in his landmark book On Growth and Form (see Keller, 2002, for a historical analysis). One of his most influential contributions was the ‘theory of transformations’, which showed how forms of different species could be geometrically related to each other. The theory of transformations was extended to relate younger and older forms of a developing organism (Richards & Kavanagh, 1945), but did not incorporate the formation and differentiation of new organs. This limitation was addressed a quarter of a century later by Lindenmayer (1968, 1971), who introduced an original mathematical formalism, subsequently called L-systems, to describe the development of linear and branching structures at the cellular level. By the mid 1970s, computational models based on Lsystems and other formalisms had been applied to study several aspects of plant development, including the development of leaves and inflorescences, and the formation of phyllotactic patterns (Lindenmayer, 1978). The questions being asked included the impact of distinct modes of information transfer (lineage vs interaction) on plant development, and the relationship between local development and global form. Similar interests underlied the independent pioneering work of Honda and co-workers on the modeling of trees (Honda, 1971; Borchert & Honda, 1984).

Another class of models was pioneered by Turing (1952), who showed mathematically that, in a system of two or more diffusing reagents, a pattern of high and low concentrations may spontaneously emerge from an initially uniform distribution. This was a surprising result, as it appeared to contradict the second law of thermodynamics: the general tendency of systems to proceed from more organized states toward disorder (the apparent paradox is resolved by jointly considering the reaction–diffusion system and its surroundings). Related models were introduced, under the name of activator–inhibitor and activator-substrate (depletion) systems, by Gierer & Meinhardt (1972), and extensively investigated by Meinhardt (1982). Reaction–diffusion systems showed how, in principle, molecular-level interactions may lead to morphogenesis and differentiation. In plants, reaction– diffusion-type models have been used to explain the patterning of trichomes in leaves and hair cells in roots (Digiuni et al., 2008; Savage et al., 2008; Jo¨nsson & Krupinski, 2010; Benı´tez et al., 2011). Nevertheless, the extent to which reaction–diffusion models apply to the plant kingdom appears to be limited (Kepinski & Leyser, 2005; Berleth et al., 2007). A significant role is played instead by mechanisms involving active transport of the plant hormone auxin (Section V). In some cases, such as the generation of phyllotactic patterns, this reliance on active transport is difficult to explain in evolutionary terms, as reaction–diffusion systems can generate the same patterns. Spatio-temporal coordination of other developmental processes, however, such as bud activation, requires long-distance signaling. Active transport may thus have evolved to overcome the limitations of diffusion, which is very slow over long distances (Crick, 1971).

In the last decade, computational modeling has become a mainstream technique in developmental plant biology, as reflected in numerous reviews (e.g. Prusinkiewicz, 2004b; Prusinkiewicz & Rolland-Lagan, 2006; Grieneisen & Scheres, 2009; Chickarmane et al., 2010; Jo¨nsson&Krupinski, 2010; Jo¨nsson et al., 2012). On the one hand, the sequencing of the human genome put in focus the chasm between knowing the genome of an organism and understanding how this organismdevelops and functions.Computational models bridge this chasm. On the other hand, successes of early conceptual models that relate patterns of gene expression to the form of animals (Lawrence, 1992) and plants (Coen & Meyerowitz, 1991) have prompted a quest for a comprehensive, mechanistic understanding of development (Coen, 1999). Current experimental techniques for tracking growth and observing marked proteins in living tissues (Reddy et al., 2004; Fernandez et al., 2010) are yielding a wealth of data that correlate molecular-level processes with plant development and form. Computational models play an increasingly important role in interpreting these data.

The use of models has been accelerated by the advancements in computer hardware, software, and modeling methodologies. General-purpose mathematical software (e.g. Mathematica and MATLAB), modeling programs built on the basis of this software (e.g. GFtbox, Kennaway et al., 2011) and specialized packages for modeling plants (e.g. the Virtual Laboratory and L-studio (Prusinkiewicz, 2004a), OpenAlea (Pradal et al., 2008) and VirtualLeaf (Merks et al., 2011)) facilitate model construction, compared with general-purpose programming languages. Furthermore, current computers are sufficiently fast to simulate and visualize many models at interactive or close-to-interactive rates, which is convenient for model exploration.


From The reaction-diffusion system: a mechanism for autonomous pattern formation in the animal skin

In his paper entitled ‘The chemical basis of morphogenesis’ Turing presented a ground-breaking idea that a combination of reaction and diffusion can generate spatial patterns (Turing 1952). In the paper, he studied the behaviour of a complex system in which two substances interact with each other and diffuse at different diffusion rates, which is known as the reaction–diffusion (RD) system. Turing proved mathematically that such system is able to form some characteristic spatio-temporal patterns in the field. One of the most significant deviations is s formation of a stable periodic pattern. He stated that the spatial pattern generated by the system might provide positional information for a developing embryo.

In spite of the importance of the idea in the developmental biology, his model was not accepted by most experimental biologists mainly because there were no experimental technologies available to test it. Therefore, most of those who took over and developed the Turing’s idea were applied mathematicians and physicists. They proposed various types of model that developed Turing’s original equation to fit real, naturally occurring phenomena (Meinhardt 1982; Murray & Myerscough 1991; Murray 1993; Nagorcka & Mooney 1992). Although the equations for each model differ, they all share the basic requirement of the original model; that is, ‘waves’ are made from the interactions of two putative chemical substances which we refer to here as the ‘activator’ and the ‘inhibitor’ (Meinhardt 1982).


Key Terms

  • Development Biology
  • Mathematical Biology
  • Biomathematics
  • Morphogenesis
  • Phyllotaxis
  • Evolutionary Biology
  • Nonlinear dynamical systems
  • Cellular Automata
  • Fractals
  • Iterated Systems
  • L-Systems
  • Pattern Formation
  • IFS (Iterated Functions Set)
  • Theoretical Biology
  • diffusion–reaction (DR) model
  • Systems Biology
  • Code Biology
  • Computational Biology
  • Algorithmic Biology
  • Complex Systems
  • Turing Patterns



Key People:

  • D’Arcy Wentworth Thompson
  • Aristid Lindenmayer
  • Alan Turing
  • Hans Meinhardt
  • Philip Ball
  • Przemyslaw Prusinkiewicz
  • Murray JD
  • Stephen Wolfram



Key Sources of Research:


On Growth and Form

Thompson D’Arcy W.




The Algorithmic Beauty of Plants

Prusinkiewicz, Przemyslaw, Lindenmayer, Aristid



The Algorithmic Beauty of Seashells

Meinhardt H, Prusinkiewicz P, Fowler D


(Springer, New York), 3rd Ed.



The Algorithmic Beauty of Seaweeds, Sponges and Corals

Kaandorp, Jaap A., Kübler, Janet E.



Mathematical Biology

Murray JD




Models of biological pattern formation

Meinhardt H




The chemical basis of morphogenesis.

Turing A


Click to access Turing.pdf



Pattern formation by coupled oscillations: The pigmentation patterns on the shells of molluscs

Hans Meinhardt, Martin Klingler



The Self-Made Tapestry Pattern formation in nature

Philip Ball




Models of biological pattern formation in space and time

Hans Meinhardt


Click to access Meinhardt.pdf



Models of biological pattern formation

Hans Meinhardt,

Click to access Hans_Meinhardt.pdf




Cellular Automata, PDEs, and Pattern Formation


Click to access 1003.1983.pdf



The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation

By Gary William Flake



The Curves of Life

Cook, T


Dover Publications, Inc. New York.



Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation

Shigeru Kondo1* and Takashi Miura


Click to access reaction-diffusion_model_as_a_framework_for_understanding_biological_pattern_formation.pdf

Click to access kondomiura10science.pdf



The Hegemony of Molecular Biology



Click to access kitcher99-hegemony.pdf



Modeling seashells


Deborah R. Fowlery􏰣, Hans Meinhardtz and Przemyslaw Prusinkiewicz

Click to access shells.sig92.pdf



The neural origins of shell structure and pattern in aquatic mollusks

Alistair Boettigera, Bard Ermentroutb, and George Oster


Click to access 6837.full.pdf



Mechanical basis of morphogenesis and convergent evolution of spiny seashells

Régis Chirata, Derek E. Moultonb,1, and Alain Goriely



Click to access 6015.full.pdf



The Geometry and Pigmentation of Seashells

S Coombes


Click to access Seashells09.pdf




Richie Khandelwal

Sahil Sahni


Click to access P7.pdf



Forging patterns and making waves from biology to geology: a commentary on Turing (1952) ‘The chemical basis of morphogenesis’

Philip Ball


Click to access f989a13264a455ec2898ed361b1c435b5f0c.pdf



Mollusc Shell Pigmentation: Cellular Automaton Simulations and Evidence for Undecidability




Click to access KuschMarkus1996.pdf



Pattern Formation in Reaction-Diffusion Systems

Masayasu Mimura


Click to access 7adbe7e696d4ba9ad3a89fed4ba15549a091.pdf



The Natural 3D Spiral

Gur Harary and Ayellet Tal


Click to access 11-HararyTal.pdf



A Model for Pattern Formation on the Shells of Molluscs



Click to access Meinhardt_1987.pdf




The reaction-diffusion system: a mechanism for autonomous pattern formation in the animal skin


Shigeru Kondo

Click to access The%20reaction-diffusion%20system_%20a%20mechanism%20for%20autonomous.pdf



Mechanical growth and morphogenesis of seashells

Derek E. Moulton, Alain Goriely and R ́egis Chirat


Click to access finalOR01.pdf



Scaling of morphogenetic patterns in continuous and discrete models


Click to access RasolonjanaharyMan_Sep2013_17293.pdf



On the Dynamics of a Forced Reaction-Diffusion Model for Biological Pattern Formation

A A Tsonis, JB Elsner, P A Tsonis

Click to access TsonisElsnerTsonis1989.pdf




A Model for Pattern Formation on the Shells of Molluscs


Click to access 5_doc.pdf



Impact of Turing’s Work


Click to access 172.pdf



The possible role of reaction–diffusion in leaf shape

Nigel R. Franks1* and Nicholas F. Britton


Click to access 10972123.pdf



Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism

Motoomi Yamaguchi*†, Eiichi Yoshimoto‡, and Shigeru Kondo


Click to access yamaguchi2007.pdf



Turing Patterns

P Ball

Click to access Turing_long.pdf






Click to access kjp006.pdf




Web Resource for Algorithmic Botony




Nicoletta Sala


Click to access ijrras_16_4_09.pdf



The Geometry of Seashells

Dr S Coombes


Click to access SeaShells.pdf






Click to access article.pdf



Models for the morphogenesis of the molluscan shell


Click to access molluscanshell.pdf



Modeling Seashell Morphology


Click to access AE-MKMpre.pdf



Exploring Complex Forms in Nature Through Mathematical Modeling: A Case on Turritella Terebra


Click to access ecaade2009_164.content.pdf



The Neural Origins of Sea Shell Patterns

Click to access Shells.pdf



Biological Pattern Formation : from Basic Mechanisms to Complex Structures

A. J. Kochy and H. Meinhardt



Form-Optimizing in Biological Structures The Morphology of Seashells

EDGAR STACH University of Tennessee



A Theory of Biological Pattern Formation

A. Gierer and H. Meinhardt



Click to access gierer_meinhardt.pdf



Cellular Automata as Models of Complexity

Stephen Wolfram,

Nature 311 (5985): 419–424, 1984

Click to access 006_Wolfram1984.pdf



Website on Oliva Porphyria



Evolution of patterns on Conus shells

Zhenqiang Gonga, Nichilos J. Matzkeb, Bard Ermentroutc, Dawn Songa, Jann E. Vendettib, Montgomery Slatkinb, and George Oster


Click to access 2012%20Evolution%20of%20patterns%20on%20Conus%20shells%20_E234.full.pdf



Theoretical aspects of pattern formation and neuronal development



20+ Photos Of Geometrical Plants For Symmetry Lovers



Computational models of plant development and form

Przemyslaw Prusinkiewicz and Adam Runions


Click to access tansley.np2012.pdf



Periodic pattern formation in reaction–diffusion systems: An introduction for numerical simulation

Takashi Miura* and Philip K. Maini


Click to access 173.pdf



Dynamics of Complex Systems

Yaneer Bar-yam