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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.
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==
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[[Image:lwss.gif|framed|left|The lightweight spaceship has speed c/2 because it moves 2 cells in 4 generations]]
For [[spaceship]]s, 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:
[[Image:speed_formula.png|center]]
 
This definition can be generalized in a straightforward manner to cellular automata with dimension other than two.


==See also==
==See also==

Revision as of 07:32, 17 August 2010

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.

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See also

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