Conway's Game of Life The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further ...

(and related

cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

), the speed of light is a propagation rate across the grid of exactly one step (either horizontally, vertically or diagonally) per generation. In a single generation, a cell can only influence its nearest neighbours, and so the speed of light (by analogy with the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

in physics) is the maximum rate at which

information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...

can propagate. It is therefore an upper bound to the speed at which any pattern can move.

Notation

As in physics, the speed of light is represented with the letter ''c''. This in turn is used as a reference for describing the average propagation speed of any given type of spaceship. For example, a

glider Glider may refer to: Aircraft and transport Aircraft * Glider (aircraft), heavier-than-air aircraft primarily intended for unpowered flight ** Glider (sailplane), a rigid-winged glider aircraft with an undercarriage, used in the sport of glidin ...

is said to have a speed of ''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 ''c''/2, as it takes four generations for a given state to be translated by two cells.

Lightspeed propagation

While ''c'' is an absolute upper bound to propagation speed, the maximum speed of a spaceship in Conway's Game of Life is ''c''/2. This is because it is impossible to build a spaceship that can move every generation. (This is not true, though, for cellular automata in general; for instance, many light-speed spaceships exist in

Seeds A seed is an embryonic plant enclosed in a protective outer covering, along with a food reserve. The formation of the seed is a part of the process of reproduction in seed plants, the spermatophytes, including the gymnosperm and angiosperm pl ...

.) It is, however, possible for objects to travel at the speed of light if they move through a medium other than empty space. Such media include trails of

hives Hives, also known as urticaria, is a kind of skin rash with red, raised, itchy bumps. Hives may burn or sting. The patches of rash may appear on different body parts, with variable duration from minutes to days, and does not leave any long-lasti ...

, and alternating stripes of live and dead cells.

Faster than light propagation

Certain patterns can appear to move at a speed greater than one cell per generation, but like faster than light phenomena in physics this is illusory. An example is the "Star Gate", an arrangement of three converging gliders that will mutually annihilate on collision. If a lightweight spaceship (LWSS) hits the colliding gliders, it will appear to move forwards by 11 cells in only 6 generations, and thus travel faster than light. This illusion happens because the glider annihilation reaction proceeds by the creation and soon-after destruction of another LWSS. When the incoming LWSS hits the colliding gliders, it isn't transported, but instead modifies the reaction so that the newly created LWSS can survive. The only signal being transmitted is that determining whether the outgoing LWSS should survive or not. This does not need to reach its destination until after the LWSS has been "transported", and so no information needs to travel faster than light.

References

{{DEFAULTSORT:Speed Of Light (Cellular Automaton) Cellular automata