Ben Jacobsohn is a rising junior physics major at the University of Maryland. He has interests in a wide variety of sciences and has experience in programming, math, physics, biology, and engineering. He is a jazz saxophonist, competitive gamer, casual athlete, and avid reader. Ben hopes to use the ideas from A New Kind of Science to discover the truly fundamental rules of the universe but is also interested in advancing artificial intelligence and cybernetically augmenting our own minds.
Computational Essay: Sensitivity of Cellular Automata to Initial Conditions
The goal of this project is to take a cellular automaton rule and find other automata with similar behavior.
Summary of Results
Incrementing is done by taking the pieces of the rule that are applied the least and changing them incrementally. Cellular automaton rules take the form of several blocks of numbers representing possible color combinations for pieces of the automaton, along with their respective color replacements. Each block of a row of the automaton is then replaced by the specified color on the next row. This means that the applications of each rule block can easily be counted, allowing more or less significant blocks to be changed. By sequentially changing the least few significant pieces of the rule, cellular automata were generally changed slightly by each step, allowing for arbitrarily large behavior changes after replacing several rule blocks. The amount of change between each was also able to be controlled fairly effectively by using more or less significant pieces of the rule.
In the future, this method of finding similarities could be used to define gradient descent over the space of cellular automata. This would allow for machine learning using cellular automata and could probably be applied to other systems as well.