Modeling Nature March 2009 1 Modeling Nature LECTURE

Modeling Nature March 2009 1

Modeling Nature LECTURE 6: Self-Organisation 2

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 3

Percolation and Ising Model revisited 4

Percolation • Given the probability p of an occupied site • What is the size M(p) of the largest connected cluster? p = 0. 30 p = 0. 45 p = 0. 55 p = 0. 70 • Clearly, M(p) grows with p 5

next neighbor interaction 6

Forest fires on a square lattice Number of rows L 7

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

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

2 D Ising model Spontaneous magnetization 10

Phase transition m +1 Tc T -1 Zero temperature (deterministic) High temperature (stochastic) • 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) 11

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

Self-Organization and Global or Local interactions 13

Self-organization Definition • 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 Web http: //pespmc 1. vub. ac. be/SELFORG. html 14

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 15

Hierarchical organization of cooperations 16

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

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. 18

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

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 ! 20

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

‘Metal leaves’ produced during the electrochemical deposition of Zn. SO 4 22

Pattern of colonial bacteria cooperative self-organization 23 Paenibacillus vortex

Colonial cooperative bacteria: patterns of self-organization Paenibacillus dendritiformis 24

Self. Organization in Insect Societies 25

Biology: Ant Self-Organization 26

Biology: Flocking http: //www. red 3 d. com/cwr/boids/ 27

Boids Software Robots that emulate flocking behaviour with simple local rules 28

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. 29

Self-organization in the brain • Orientation sensitivity 30

Self-organization in the brain • Direction tuning 31

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

Self-Organization: synchronization 33

Synchronization of clapping 34

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

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

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

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 Mc. Clintock, Menstrual synchrony and suppression. Nature. 1971; 291: pp. 244 -245. 38

Self-Organization in social dynamics 39

Mexican Wave 40

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

Sociology: Escape Dynamics 42

Sociology: Escape Dynamics 43

Sociology: Escape Dynamics 44

Mexican-Wave demo http: //angel. elte. hu/wave Lane formation and other demo’s http: //www. helbing. org/ Steering behaviour for Autonomous Characters www. red 3 d. com/cwr/steer 45

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 • … 46

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

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

END of COURSE 49