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Modeling Nature March 2009

Modeling Nature March 2009. Modeling Nature. LECTURE 6: Self-Organisation. Overview. Percolation and Ising spin models Definition of self-organization Local and global interaction Natural patterns Flocking and Boids Synchronization of clapping and fireflies

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Modeling Nature March 2009

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  1. Modeling NatureMarch 2009

  2. Modeling Nature LECTURE 6: Self-Organisation

  3. Overview • Percolation and Ising spin models • Definition of self-organization • Local and global interaction • Natural patterns • Flocking and Boids • Synchronization of clapping and fireflies • Self-organization in social dynamics

  4. Percolation and Ising Model revisited

  5. p = 0.30 p = 0.45 p = 0.55 p = 0.70 Percolation • Given the probability p of an occupied site • What is the size M(p) of the largest connected cluster? • Clearly, M(p) grows with p

  6. next neighbor interaction

  7. Forest fires on a square lattice Number of rows L

  8. p < pc p  pc p > pc scale Small scale Large scale At pC the forest is a fractal zooming out

  9. S N -1 +1 coupling +1 +1 N S The Ising model

  10. 2D Ising model Spontaneous magnetization

  11. m +1 Tc T -1 Phase transition • At a critical value of T, Tc, the behaviour of the systems changes (it becomes critical) • The critical behaviour is characteristic for the system (and other systems) High temperature (stochastic) Zero temperature (deterministic)

  12. Ising and Percolation models Macroscopic Effects are entirely determined by LOCAL INTERACTIONS • Local microscopic interactions (with nearest neighbour) • Global macroscopic structure/patterns

  13. Self-Organizationand Global or Local interactions

  14. Self-organizationDefinition • Self-organization is a process where the organization of a system spontaneously increases, i.e., without this increase being controlled by the environment or an encompassing or otherwise external system. Principia Cybernetica Webhttp://pespmc1.vub.ac.be/SELFORG.html

  15. Self-Organization 1. GLOBAL INTERACTIONS A director/manager/conductor coordinates and controls the numerous microcopic processes such that global order arises Perhaps in a hierarchical network

  16. Hierarchical organization of cooperations

  17. Five-Year Plans for the National Economy of the Soviet Union

  18. Organization of consciousness: Homunculus Diagram from Descartes' Treatise of Man (1664), showing the formation of inverted retinal images in the eyes, and the transmission of these images, via the nerves so as to form a single, re-inverted image (an idea) on the surface of the pineal gland.

  19. Organization of consciousness: Homunculus Problem with Descartes' Homunculus: how is the consciousness of the homunculus itself organized?

  20. Self-Organization 2. LOCAL INTERACTIONS There is no director/manager/conductor that coordinates or controls the global order, it ‘spontaneously’ arises from local interactions, e.g. next-neighbor-interactions. THERE IS NO CENTRAL ORGANIZATION !

  21. Patterns from local interactions in inanimate Nature: snow flakes.

  22. ‘Metal leaves’ produced during the electrochemical deposition of ZnSO4

  23. Pattern of colonial bacteria cooperative self-organization Paenibacillus vortex

  24. Colonial cooperative bacteria: patterns of self-organization Paenibacillusdendritiformis

  25. Self-Organization in Insect Societies

  26. Biology: Ant Self-Organization

  27. Biology: Flocking http://www.red3d.com/cwr/boids/

  28. Boids Software Robots that emulate flocking behaviour with simple localrules

  29. Self-organization in the brain The brain consists of +/- 1011 neurons connected in a large network where each neuron is connected to only a handfull other neurons There is no central organization, only local interactions.

  30. Self-organization in the brain • Orientation sensitivity

  31. Self-organization in the brain • Direction tuning

  32. Lion King sequence • Simulation stampede simulated using “boid” techniques

  33. Self-Organization: synchronization

  34. Synchronization of clapping

  35. Period doubling Self-organization of clapping Global noise intensity Local noise intensity Correlation parameter Average noise intensity Clapping period

  36. rhythmic asynchronous rhythmic asynchronous Audience of 73 persons Audience of single person Period doubling • Transition from asynchronous to rhythmic clapping: skip every second beat • Yields a clapping mode with a double period

  37. Firefly Synchronization • Fireflies will synchronize their flashes based on their observations of their neighbor’s rhythm. • Entire riversides thus flash simultaneous

  38. Menstrual cycle Synchronization Women who live together tend to have synchronized menstrual periods. The phenomenon was first presented to the scientific community almost 40 years ago, and has since remained a matter of much debate. There is still much controversy over what is the cause. • Martha McClintock, Menstrual synchrony and suppression. Nature. 1971; 291: pp. 244-245.

  39. Self-Organization in social dynamics

  40. Mexican Wave

  41. Critical mass is needed for onset of MW Mexican-Wave model http://angel.elte.hu/wave Mexican-Wave demo

  42. Sociology: Escape Dynamics

  43. Sociology: Escape Dynamics

  44. Sociology: Escape Dynamics

  45. Lane formation and other demo’s Mexican-Wave demo http://angel.elte.hu/wave http://www.helbing.org/ Steering behaviour for Autonomous Characters www.red3d.com/cwr/steer

  46. Issues in self-organisation • Self-organizing processes underlie patterns in nature, society, and culture • What is the relation between individual behavior and collective behavior? • Not always obvious, e.g., termite behaviour • Nature evolves group behaviors that improve fitness • Society evolves group behaviors that improve social acceptance • …

  47. Relation to the Tasks Task 6a.Emergent Structure – How does global and macroscopic structure arise from interactions that are strictly local?

  48. Relation to the Tasks Task 6b. Complex models of self-organisation

  49. END of COURSE

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