Cellular Automata

• Discrete CAs

• Continuous Cas

• Fluids

• CA Rules

• Life-like Rules

Discrete Cellular Automata

Discrete Cellular Automata

Continuous Cellular Automata

Any level of grey between white (O) and black (1)

Example : 3 cells [0.7, 0.8, 0.9]

0.7 + 0.8 + 0.9)/3 = 0.8 0.8 + 0.9 = 1.7 0.7

Continuous Cellular Automata

http://demonstrations.wolfram.com/ContinuousCellularAutomatonWithMathRulesII/

Fluids

http://demonstrations.wolfram.com/CellularAutomatonFluids/

Cellular Automata RulesGeneral rule

The Moore neighbourhood

Cellular Automata RulesConway's Game of Life

• Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.

• Any live cell with more than three live neighbours dies, as if by overcrowding.

• Any live cell with two or three live neighbours lives on to the next generation.

• Any dead cell with exactly three live neighbours becomes a live cell.

Cellular Automata RulesConway's Game of Life

Cellular Automata RulesBrian’s Brain

Dead Alive Dying

Cellular Automata RulesLangton’s ant

• At a white square, turn 90°right, flip the color o f the square, move forward one unit.

• At a black square, turn 90°left, flip the color of the square, move forward one unit.

Langton's ant

after 11000 steps.

A red pixel shows

the ant's location.

Cellular Automata RulesLangton’s ant

Cellular Automata RulesLangton’s ant

Grows chaotically Creates a convoluted highway Fills space in a square around itself

Spiral growth Semi-chaotic growth Chaotic growth with a distinctive texture

Growth with a distinctive texture inside an expanding

frame

Constructing a Fibanocci spiral

Cellular Automata RulesWireworld

http://people.bath.ac.uk/amg24/ma10126/wireworld/runsim.html?pattern=2

Background (empty) cells, which do not change

Conductor (wire) cells, which change into electron heads if exactly one or two of their neighbours are electron heads.

Electron heads, which change into electron tails.

Electron tails, which change into wire.

Clocks Diode

A clock is a simple circuit that

repeatedly sends out electrons in

a regular pattern

Those images show how an electron passes through

a diode.

Life-like Rules

A Cellular Automata is Life-like (in the sense of being similar to Conway's Game of Life) if it meets the following criteria:

• The CA has two dimensions

• The CA has two states (called OFF and ON)

• The neighborhood is the Moore neighbourhood

• The new state of the cell in the next generation can be expressed as a function of the number of adjacent cells that are in the ON state and the cell's own state

http://www.collidoscope.com/modernca/lifelikerules.html