# Speed

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, for first neighbor neighborhoods, is a rate of one cell per generation. The speed of light is the fastest possible speed at which any effect can propagate.

## Spaceships

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.

## See also

## External links

- Spaceships at Wikipedia

- Speed of light at the Life Lexicon