Seeds (cellular automaton)

Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of infinite two-dimensional grid of cells, each of which may be in one of two states: "on" or "off". Each cell is considered to have eight neighbors (Moore neighbourhood), as in Life. In each time step, a cell turns on if it was off but had exactly two neighors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule M:/2.

In Game of Life terminology, a pattern in which all cells that were on turn off at each step is called a "phoenix". All patterns in Seeds have this form.

Even though all live cells are constantly dying, the small birth requirement of two cells means that nearly every pattern in Seeds explodes into a chaotic mess that grows to cover the entire universe. However, some patterns are known that behave in a more controlled fashion, repeating the same shape either in the same position of the grid (an oscillator) or translated some number of grid units after several steps (a spaceship). More complex rake and puffer patterns are known which move like spaceships leaving trails of oscillators or other spaceships behind them. Most of these patterns move at a speed of one cell per time step (the so-called "speed of light") including three commonly seen spaceships with four on cells each, but slower-moving patterns are also known. A [http://entropymine.com/jason/life/alt/b2s.zip collection of patterns for the Seeds rule] collected by Jason Summers includes patterns found by Stephen Wright, Mirek Wójtowicz, Noam Elkies, Mark Niemiec, Peter Naszvadi, and David Eppstein.

External links

*cite web
author = David Eppstein
url = http://fano.ics.uci.edu/ca/rules/b2s/
title = Known spaceships for the Seeds rule

*cite web
author = Alan Hensel
url = http://www.radicaleye.com/lifepage/glossary.html
title = A Brief Illustrated Glossary of Terms in Conway's Game of Life

*cite web
author = Brian Silverman
year = 1996
title = Changing the Rules
url = http://www.maa.org/editorial/mathgames/seeds.html
work = [http://www.maa.org/editorial/mathgames/index.html The Virtual Computer]

* cite web
author = Mirek Wójtowicz
url = http://www.mirwoj.opus.chelm.pl/ca/rullex_life.html
title = Cellular Automaton Rules Lexicon — Family: Life
work = Mirek's Cellebration