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 • Self-organization in social dynamics
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
Forest fires on a square lattice Number of rows L
p < pc p pc p > pc scale Small scale Large scale At pC the forest is a fractal zooming out
S N -1 +1 coupling +1 +1 N S The Ising model
2D Ising model Spontaneous magnetization
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)
Ising and Percolation models Macroscopic Effects are entirely determined by LOCAL INTERACTIONS • Local microscopic interactions (with nearest neighbour) • Global macroscopic structure/patterns
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
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
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.
Organization of consciousness: Homunculus Problem with Descartes' Homunculus: how is the consciousness of the homunculus itself organized?
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 !
‘Metal leaves’ produced during the electrochemical deposition of ZnSO4
Pattern of colonial bacteria cooperative self-organization Paenibacillus vortex
Colonial cooperative bacteria: patterns of self-organization Paenibacillusdendritiformis
Biology: Flocking http://www.red3d.com/cwr/boids/
Boids Software Robots that emulate flocking behaviour with simple localrules
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.
Self-organization in the brain • Orientation sensitivity
Self-organization in the brain • Direction tuning
Lion King sequence • Simulation stampede simulated using “boid” techniques
Period doubling Self-organization of clapping Global noise intensity Local noise intensity Correlation parameter Average noise intensity Clapping period
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
Firefly Synchronization • Fireflies will synchronize their flashes based on their observations of their neighbor’s rhythm. • Entire riversides thus flash simultaneous
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.
Critical mass is needed for onset of MW Mexican-Wave model http://angel.elte.hu/wave Mexican-Wave demo
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
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 • …
Relation to the Tasks Task 6a.Emergent Structure – How does global and macroscopic structure arise from interactions that are strictly local?
Relation to the Tasks Task 6b. Complex models of self-organisation