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Orthogonal speeds of spaceships. Note: This image is outdated as it does not include 31c/240, c/10 nor 3c/7 orthogonal.

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 in the Moore and von Neumann neighbourhoods of range 1, although patterns in certain rules with Larger than Life neighbourhoods can break this barrier.


The lightweight spaceship has speed c/2 because it moves 2 cells in 4 generations

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:

Speed formula.png

This definition can be generalized in a straightforward manner to cellular automata with dimension other than two.

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