Lace: A New Kind of Cellular Automata Where Links Matter

Summary

This article is about a new kind of simple computational rule (“LACE rules” running on LACE, the Link Automata Computing Engine platform) which, when applied locally on a grid of cells, demonstrates fascinating emergent “artificial life” behavior. For readers familiar with the Game of Life (GOL), this is a next-level class of cellular automata that utilizes neighborhood topology — the state of the grid is a function of both cell states and their connectivity (links).To quickly get a sense of what LACE does – scroll down in this post to the video Gallery section and take a look at (a) the Game of Life, with links, and then as a comparison, check out (b) the “Amazing Dragons” LACE rule, and the many other “Realm of LACE” (ROL) rules that fully utilize topology. Preamble I have been thinking about cellular automata ever since I read a fascinating and important book, Three Scientists and Their Gods, during the summer of my sophomore year of college. This book changed my life. After reading this book ferociously on the drive home from Oberlin college to Boston, for summer vacation, I became obsessed with the idea of digital physics – and particularly with the work of Ed Fredkin, (and later Stephen Wolfram as well). In fact, this idea captivated me so much that I thought about it night and day, until one afternoon, I actually had what I can only call “a vision” about it. I had come back from lunch with my father, where our conversation had been about whether a cellular automata could model a mouse brain. After lunch I went upstairs and tried to write some code to model a simple brain this way. Then, to take a break, I decided to go outside and paint (another interest of mine at the time). It was a hot summer day in Boston. My subject was a simple nondescript raspberry bush in my front yard. As I painted, I entered a kind of non-conceptual state – a trance of concentration. And gradually, instead of seeing the leaves, I saw the spaces between them. So I painted around the ...