cellular automata rules
DESCRIPTION
discrete ca, continuous ca, ca rules, fluids, life-like rulesTRANSCRIPT
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