The speed of a pattern is a measure of the number of generations that it takes for some effect to travel some given distance. Speeds are almost always measured in reference to the speed of light (or speed of life), denoted by c which, the fastest possible speed at which any effect can propagate; for first neighbor neighborhoods, such as the Moore and von Neumann neighbourhoods of range 1, this is a rate of one cell per generation. Rules with extended neighbourhoods, such as Larger than Life rules, have higher speeds of light. Such speeds can be defined as the rule's "relative lightspeed", with one cell per generation being defined as "absolute lightspeed".
For spaceships, the speed describes the number of cells that it has been displaced by after it has gone through one period. Speed is reported in the form dc/p where d is the displacement and p is the period. It is most common to reduce this "fraction" to lowest terms. For example, even though the period of a lightweight spaceship is 4, it moves 2 cells during those generations, giving it a speed of 2c/4 = c/2.
For spaceships that move diagonally, speed is defined the same as above, but where "the number of cells that is has been displaced by" refers to the maximum of the x or y displacement; not their sum. So, for example, a glider has a speed of c/4, since it takes 4 generations to move one cell in the x direction and one cell in the y direction.
More formally, if a spaceship in any 2D cellular automaton is translated by (x,y) after n generations then its speed v may be defined as:
This definition can be generalized in a straightforward manner to cellular automata with dimension other than two.
- Speed of light at the Life Lexicon