Self-Organization in Natural Systems

Self-Organization in Natural Systems MANO Jean Pierre

Self-Organization in Natural Systems • What are the mechanisms for integrating subunits into a coherently structured entity?

Self-Organization in Natural Systems • What are the mechanisms for integrating subunits activity into a coherently structured entity? • From simple neurons to the thinking brain • From individuals to the society • From molecule to pattern

Self-Organization in Natural Systems • What are the mechanisms for integrating subunits activity into a coherently structured entity? • From simple neurons to the thinking brain • From individuals to the society • From molecule to pattern C3H4O4 NaBr NaBrO3 HSO3 C12H8N2SO2Fe Malonic acid Sodium bromide Sodium bromate Sulfuric acid 1,10 Phenanthroline ferrous sulfate

Self-Organization in Natural Systems • Definitions • Pattern formation In living and non-living systems • Social systems Sociality and gregarism • Cellular systems Cells build animals • Properties of self-organized systems

Definitions • What is Chaos ? [Poincarré] [Lorenz] [Prigogine] disorder, confusion, is opposed to order and method “Chaos” define a particular state of a system that is characterized by the following behaviors: • Do not repeat • Sensible to initial conditions: sharp differences can produce wide divergent results • Moreover, ordered and characterized by an unpredictable determinism • When moving away from equillibrium state => high organization • Non equillibrium phasis: bifurcations • Amplification => Symetry break

Definitions • What is Self-organization in natural systems? Self-organization is a process in which pattern at the global level of a system emerges solely from numerous interactions among the lower level components of the system. [Deneubourg 1977] Moreover, the rules specifying interactions among the system’s components are executed using only local information, without reference to the global pattern In other words, the pattern is an emergent property of the system, rather than a property imposed on the system by an external influence

Definitions • What is an emergent property ? • Many Agents • Simple rules • Many interactions • Decentralization • Emergent properties • Unreductibility • Macro-level (odre magnitude difference) • Feed-back effect on the micro-level Conditions Observations

Self-Organization in Natural Systems • Definitions • Pattern formation In living and non-living systems • Social systems Sociality and gregarism • Cellular systems Cells build animals • Properties of self-organized systems

Non-living pattern formation • Based on physical and chemical properties • Belousov-Zhabotinsky reaction • Bénard convection cells • Sand dune ripples • Glass cracks • Mud cracks

Pattern formation in biological systems • Patterns characterizing individuals • Giraffe coat • Zebra • Leopard • Vermiculated rabbitfish • Cone shells • Finger prints • Morel • Metamerization • Occular dominance stripes

Pattern formation in biological systems • Patterns characterizing individuals • Giraffe coat • Zebra • Leopard • Vermiculated rabbitfish • Cone shells • Finger prints • Morel • Metamerisation • Occular dominance stripes

Pattern formation in biological systems • Most of those patterns are in fact fixed states of reactions that have occurred long time ago… • Patterns characterizing individuals • Giraffe coat • Zebra • Leopard • Vermiculated rabbitfish • Cone shells • Finger prints • Morel • Metamerisation • Occular dominance stripes

Pattern formation in biological systems • Most of those patterns are in fact fixed states of reactions that have occurred long time ago… • Patterns characterizing individuals • Giraffe coat • Zebra • Leopard • Vermiculated rabbitfish • Cone shells • Finger prints • Morel • Metamerisation • Occular dominance stripes … or process is still running. Mechanisms ?

Degradation Degradation Slow diffusion ACTIVATOR ACTIVATEUR INHIBITOR INHIBITEUR Quick diffusion + + - Activation-inhibition mechanism autocatalyzis Inspired by equations of reaction-diffusion [Turing1949] inhibition The activator autocatalyzes its own production, and also activates the inhibitor. The inhibitor disrupts the autocatalytic process. Meanwhile, the two substances diffuse through the system at different rates, with the inhibitor migrating faster. The result: local activationandlong-range inhibition

Activation-inhibition mechanism Activation-inhibition and self-organization share a common mechanism Starting point: a homogeneous substrate (lacking pattern) Positive feedback (short-range activation, autocatalyzes) Negative feedback (long-range inhibition)

Self-Organization in Natural Systems • Definitions • Pattern formation In living and non-living systems • Social systems Sociality and gregarism • Cellular systems Cells build animals • Properties of self-organized systems Low dynamic High dynamic

Pattern formation in colonies activity • Patterns resulting from the activity of a society of… social insects • Ants • Bees • Wasps • Termites Mammalians • African Mole-rats • Humans

Pattern formation in colonies activity • Patterns resulting from the activity of a society of… social insects • Ant • Bees • Wasps • Termites Mammalians • African Mole-rats • Humans

Pattern formation in colonies activity • Patterns resulting from the activity of a society of… social insects • Ant • Bees • Wasps • Termites Mammalians • African Mole-rats • Humans • Several orders of size magnitude difference • Those patterns result of the permanent activity of society’s elements… Causality and mechanisms ?

Pattern formation in colonies activity Environmental constraints Openess Heterogeneity… Template Gradients Grids… Stigmergy [Grassé 1959] Indirect interactions between animals Local environmental changes (pheromones, mud pellets…)

Pattern formation in biological systems • Patterns occurring during collective movement Microorganisms Insects and Crustaceans Social insects Fishes Birds Mammalians

Self-Organization in Natural Systems