Spaceship (CA)

In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position. The smallest such number of generations is called the period of the spaceship.

The speed of a spaceship is often expressed in terms of c, the metaphorical speed of light (one cell per generation) which in many cellular automata is the fastest that an effect can spread. For example, a glider in Conway's Game of Life is said to have a speed of ${\displaystyle c/4}$, as it takes four generations for a given state to be translated by one cell. Similarly, the lightweight spaceship is said to have a speed of ${\displaystyle c/2}$, as it takes four generations for a given state to be translated by two cells. More generally, if a spaceship in a 2D automaton is translated by ${\displaystyle (x,y)}$ after ${\displaystyle n}$ generations, then the speed ${\displaystyle v}$ is defined as:

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