Understanding Multiple Neighborhood Cellular Automata

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2021-05-26 07:00:10

Multiple Neighborhood Cellular Automata (MNCA) are an extension of traditional cellular automata like Conway’s Game of Life, developed in 2014 while I was experimenting with neighborhood configurations.

MNCA produce complex emergent patterns, often featuring robust local structures similar to solitons. The unique properties of these structures offer a vast increase in the diversity of resulting phenomena in comparison to single-neighborhood cellular automata. Furthermore, the method behind MNCA can be directly applied to continuous-space models, producing similar results:

For the sake of demonstration simplicity, the MNCA referenced further in this post will be two-state ‘discrete’ models.

Traditional cellular automata like Conway’s Game of Life define a single group of local neighbors for each pixel, and sum the values at those locations. This ‘neighborhood’ is used to decide how the update functions will determine that pixel’s value for the next time-step. Unlike these traditional methods, MNCA use two or more neighborhoods of distinct composition, with each neighborhood assigned its own update functions. These updates are assessed in the order they are executed, with later updates potentially overwriting those that took place before them.

MNCA models often form structures that exhibit individualized, unit-like local identities, comparable to solitons. These structures are significantly different to those found in other cellular automata, exhibiting incredible resilience as they interact with their environment in a robust and non-destructive manner. There are a wide variety of emergent phenomena seen in MNCA that are not common in simpler models. Some observations include:

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