cellular automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tesse ...
Brian Silverman
Brian Silverman is a Canadian computer scientist, the creator of many programming environments for children, and named by Mirek Wójtowicz. It consists of an 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 neighborhood
In cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells that surround it.
Name
The neighborhood is named after Edward F. Moore, a pioneer of cellular aut ...
), as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors 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 B2/S.
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. Thus, in Wolfram's classification of cellular automata, it is a Class III automaton, in which nearly all patterns evolve chaotically..
However, some patterns are known to 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 1 cell per time step (the so-called ''
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
'', or c/1) including three commonly seen spaceships with four on cells each, but slower-moving patterns are also known. A collection of patterns for the Seeds rule collected by Jason Summers includes patterns found by Stephen Wright, Mirek Wójtowicz,
Noam Elkies
Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At the age of 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist, chess national master and a chess composer.
Ear ...
, Mark Niemiec, Peter Naszvadi, and
David Eppstein
David Arthur Eppstein (born 1963) is an American computer scientist and mathematician. He is a Distinguished Professor of computer science at the University of California, Irvine. He is known for his work in computational geometry, graph algo ...
Brian's Brain
Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule.
Rules
Brian's Brain consists of an infinite two-dimensional grid of cells, but unlike Seeds, each cell may be in one of three states: on ...