Exploring Cellular Automata: A Fascinating World of Rules and Patterns
Delve into the intricate realm of cellular automata, from elementary one-dimensional systems to the renowned Game of Life. Discover the versatility and complexity of these systems, including their capacity for simulating universes and implementing logic gates. Uncover the emergence of life-like behaviors and the potential implications for understanding our own reality.
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Presentation Transcript
Cellular Automata Avi 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 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
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 Block Beehive Loaf Boat Oscillators Blinke r Toad Beacon Glider
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
