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Exploring Mobile Automata with Non-Local Rules

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This summer, I had the incredible opportunity to attend the Wolfram High School Summer Research Program. Interested in ruliology, I focused my project on mobile automata, a type of simple program similar to cellular automata.

Mobile Automata with Non-Local Rules

In cellular automata, all cells update in parallel according to a set of rules, whereas mobile automata feature a single active cell that updates at each iteration. The rules for mobile automata dictate the new state of the active cell and its movement. These rules consider the states of the active cell and its immediate neighbors, determining the new color of the active cell and whether it moves to the left or right.


Traditionally, mobile automata involve the active cell interacting with its immediate left and right neighbors. However, in my project, I explored the effects of non-local interactions, where the dependent cells are farther away from the active cell. For instance, I examined scenarios where the dependent cells were two cells to the left and three cells to the right of the active cell.


Mobile automata can also have rules that increase the number of active cells. By implementing non-local rules in those types of rules as well, I was able to find immense complexity from a simple set of rules. Here is a picture from my project, where the black dots symbolize the active cells and the numbers on top represent the dependent cell ranges.

Some Possible Philosophical Implications


Exploring mobile automata with non-local rules opens up fascinating philosophical questions about the nature of complexity and emergence. One key question is how simple rules can lead to highly complex behaviors. This ties into the broader philosophical debate about reductionism and emergence. Can the behavior of a complex system be fully understood by examining its parts, or does the system exhibit properties that are not present in its individual components?


Furthermore, this research touches on the concept of interconnectedness. In mobile automata with non-local rules, the state of the active cell depends on cells that are not immediately adjacent, suggesting that even distant elements in a system can have significant impacts on its behavior. This idea resonates with philosophical discussions about the interconnectedness of all things in the universe, where actions in one part of a system can have far-reaching effects. This could also have implications in nonlocality seen in systems in quantum mechanics.


For More Information


For a more in-depth dive into mobile automata with non-local rules, you can check out my computational essay in the form of a Wolfram Community post here: https://community.wolfram.com/groups/-/m/t/3214519?p_p_auth=z3DG3Bp8


This essay was the final product of the whole program so it includes all of my findings and complexity regarding mobile automata with non-local rules.

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