1. Cellular Automata

2. History John von Neumann and Ulam (1940’s)
Crystal structure
Self reproducing machines
John Conway – Game of Life (1970)
Student interest
Stephen Wolfram
Cellular Automata
New Kind of Science

3. Properties Discrete, local, synchronous Grid of cells – often 2D
Symbols, often binary
Neighborhood
Moore 8 surrounding cells
Von Neumann 4 cells (orthogonally)
Rules for cell state: f(neighborhood)

4. Conway’s Game of life
Any live cell with fewer than two live neighbors dies, as if caused by underpopulation.
Any live cell with more than three live neighbors dies, as if by overcrowding.
Any live cell with two or three live neighbors lives on to the next generation.
Any dead cell with exactly three live neighbors becomes a live cell.

5. R-pentomonio

6. Still Lifes
Ship
Loaf
Beehive
Boat

7. Ocsillators
Blinker
Period 2
Toad
Period 2
Pulsar
Period 3

8. Gliders
Glider – cycle length 6
Gosper’s
Glider Gun

9. Computation Gliders for data streams Structures that act as gates
Turing Computatable

10. Wolfram Numeric description
Detailed analysis: ‘Cellular Automata and Complexity”

11. Wolfram’s results
Class 1: Nearly all initial patterns evolve quickly into a stable, homogeneous state. Any randomness in the initial pattern disappears.
Class 2: Nearly all initial patterns evolve quickly into stable or oscillating structures. Some of the randomness in the initial pattern may filtered out, but some remains. Local changes to the initial pattern tend to remain local.
Class 3: Nearly all initial patterns evolve in a pseudo-random or chaotic manner. Any stable structures that appear are quickly destroyed by the surrounding noise. Local changes to the initial pattern tend to spread indefinitely.
Class 4: Nearly all initial patterns evolve into structures that interact in complex and interesting ways. Class 2 type stable or oscillating structures may be the eventual outcome, but the number of steps required to reach this state may be very large, even when the initial pattern is relatively simple. Local changes to the initial pattern may spread indefinitely. Wolfram has conjectured that many, if not all class 4 cellular automata are capable of universal computation. This has been proved for Rule 110 and Conway's game of life.

12. New Kind of Science
Replace differential equations with cellular structures
CA become a standard fabric for constructions

13. MCell By Mirek Wojtowciz Windows app and now Java based versions
Large set of rules in families
1D systems
General binary
Larger than Life