Introduction

This is the first post on Cellular Cosmology, a research diary of sorts on the long-term and macroscopic behavior of cellular automata.

As is often the case in the lands of cellular automata, I am a hobbyist rather than anything resembling a professional (though I do have some past studies in mathematics under my belt). It seems however that, in contrast to the median hobbyist, my interests are not limited to the discovery and/or construction of “interesting patterns” — objects like oscillators, spaceships, conduits, guns, rakes, as documented by now in great detail in places such as LifeWiki — but also on the underlying reasons of why certain cellular automata behave in some way and not in some other way.

Cellular automata as we know them are mathematical models, and their software implementations, developed by humans. As such we know their fundamental rules in full detail (and we can typically predict exactly the behavior of any given pattern in any given rule). Taking the primus inter pares of CA for example, that is Conway’s Game of Life, cells are born iff they have 3 living parents and survive iff they have 2 or 3 living parents — “B2/S23” for short in CA parlance. But it remains challenging to determine why, exactly, this specific rule leads to complex behavior that has captivated audiences for over fifty years by now. At the same time, already some very similar rules, of totalistic CA with the Moore neighborhood, lead to either much sparser results (say, B35/S23) or explosive chaos (say, B3/S013), of which neither lends itself to “engineering” work quite as easily. We are thus concerning ourselves here essentially with the chaos-theoretic problem of “emergent complexity”: what is it, how it happens and why?

An initial goal I will be occupied with will be the construction of a new typology of CA that aims to be be more fine-grained than the four-fold categorization proposed by Wolfram (“dying”, “stabilizing”, “chaotic” and “complex”).