Seeds is a cellular automaton

Cellular automaton

A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...

 in the same family

Life-like cellular automaton

A cellular automaton is Life-like if it meets the following criteria:* The array of cells of the automaton has two dimensions....

 as the Game of Life

Conway's Game of Life

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....

, 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 neighborhood

Moore neighborhood

In cellular automata, the Moore neighborhood comprises the eight cells surrounding a central cell on a two-dimensional square lattice. The neighborhood is named after Edward F. Moore, a pioneer of cellular automata theory. It is one of the two most commonly used neighborhood types, the other one...

), 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. 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

Speed of light (cellular automaton)

In Conway's Game of Life , the speed of light is a propagation rate across the grid of exactly one step per generation...

) 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 Elkies

Noam David Elkies is an American mathematician and chess master.At age 14, Elkies received a gold medal with a perfect score at the International Mathematical Olympiad, the youngest ever to do so...

, Mark Niemiec, Peter Naszvadi, and David Eppstein

David Eppstein

David Arthur Eppstein is an American computer scientist and mathematician. He is professor of computer science at University of California, Irvine. He is known for his work in computational geometry, graph algorithms, and recreational mathematics.-Biography:Born in England of New Zealander...

.