Natural Computation and Self-Organization:
The Physics of Information Processing in Complex Systems
Lecture 11: Pattern Formation
Reading: Lecture Notes.
Topics:
- Review last lecture.
- Spatially extended dynamical systems
- How to make
- State space
- What does dynamical systems have to say?
- Cellular Automata
- Definitions
- Mathematical properties
- 1D CAs
- Behavior Survey
- CA Computational Mechanics: Invariant Sets, Domains, Particles
- Synchronous and Asynchronous CAs
- 2D CAs
- Simulation examples
- Nonlinear Map Lattices
- Definitions
- Mathematical properties
- 1D LDSs
- Simulation examples
- Statistical Mechanics: Spin systems
- Ising Spin System
- As a CA: Creutz Model
- Phase transition
- Simulation examples
Reading for next meeting: EIT, Chapters 1 and 2.