Cellular AutomataAvi Swartz

2015 UNC Awards Ceremony

Definition Collection of Cells with a simple set of rules and a given

starting value Proposed by John von Neumann Good programming exercise

Elementary Cellular Automaton One Dimensional Each cell is determined by its value, and the values of its

neighbors

Rule 110

Rule 110

This automaton is Turing complete and universal Can simulate any other computer or computer program Simplest known Turing complete system

Totalistic Cellular Automaton One dimensional Multicolored Cell value is determined by average of neighbors

Code 600

Game of Life Two dimensional automaton Proposed by John Conway Rules:

If a cell has 2 live neighbors, it is unchanged If a cell has 3 live neighbors, it becomes alive If a cell has fewer than 2 live neighbors, it dies If a cell has more than 3 live neighbors, it dies

Examples

Still Lifes

Oscillators

Glider

Block Beehive

Loaf Boat

Blinker

Toad Beacon

Examples

Programming with Life Wires and logic gates can be built This makes the game Turing Complete and programmable

Twin prime calculator Fermat prime calculator Recursive

Game Life vs. Real Life Exhibits emergent properties Life on Earth originated from inorganic material Could be a way of simulating life or a universe

Turing Completeness 4 rules in life, 4 forces of nature

Continuous Final Examples