Natural Computation and Self-Organization:
The Physics of Information Processing in Complex Systems

Jim Crutchfield
chaos@cse.ucdavis.edu; http://cse.ucdavis.edu/~chaos

Winter 2008
WWW: http://cse.ucdavis.edu/~chaos/courses/ncaso/

Lecture 11: Pattern Formation

Reading: Lecture Notes.
Topics:

  1. Review last lecture.
  2. Spatially extended dynamical systems
    1. How to make
    2. State space
    3. What does dynamical systems have to say?
  3. Cellular Automata
    1. Definitions
    2. Mathematical properties
    3. 1D CAs
    4. Behavior Survey
    5. CA Computational Mechanics: Invariant Sets, Domains, Particles
    6. Synchronous and Asynchronous CAs
    7. 2D CAs
    8. Simulation examples
  4. Nonlinear Map Lattices
    1. Definitions
    2. Mathematical properties
    3. 1D LDSs
    4. Simulation examples
  5. Statistical Mechanics: Spin systems
    1. Ising Spin System
    2. As a CA: Creutz Model
    3. Phase transition
    4. Simulation examples

Reading for next meeting: EIT, Chapters 1 and 2.