More complex rake and puffer patterns are known which move like spaceships leaving trails of oscillators or other spaceships behind them. Most of these patterns move at a speed of 1 cell per time step (the so-called speed of light, or c/1) including three commonly seen spaceships with four on cells each, but slower-moving patterns are also known. A collection of patterns for the Seeds rule collected by Jason Summers includes patterns found by Stephen Wright, Mirek Wójtowicz, Noam Elkies, Mark Niemiec, Peter Naszvadi, and David Eppstein. * Brian's Brain, a similar cellular automaton by the same author *
Game of LifeConway's LifeConway’s Game of Life
Later discoveries included other guns, which are stationary, and which produce gliders or other spaceships; puffer trains, which move along leaving behind a trail of debris; and rakes, which move and emit spaceships. Gosper also constructed the first pattern with an asymptotically optimal quadratic growth rate, called a breeder or lobster, which worked by leaving behind a trail of guns. It is possible for gliders to interact with other objects in interesting ways. For example, if two gliders are shot at a block in a specific position, the block will move closer to the source of the gliders. If three gliders are shot in just the right way, the block will move farther away.
cellular automataCACell games (cellular automaton)
Brian's Brain. Langton's ant. Wireworld. Rule 90. Rule 184. von Neumann cellular automata. Nobili cellular automata. Codd's cellular automaton. Langton's loops. CoDi. Firing squad synchronization problem. Majority problem. Golly. Discrete calculus. Golly. Discrete calculus. Golly. Discrete calculus. Golly. Discrete calculus. Discrete calculus. Discrete calculus. Discrete calculus. Discrete calculus. Cellular automaton FAQ from the newsgroup comp.theory.cell-automata. "Neighbourhood Survey" (includes discussion on triangular grids, and larger neighborhood CAs). von Neumann, John, 1966, The Theory of Self-reproducing Automata, A. Burks, ed., Univ. of Illinois Press, Urbana, IL.
In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position. The smallest such number of generations is called the period of the spaceship.
speed of lightc''/2cellular automaton speed of light
In Conway's Game of Life (and related cellular automata), 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 in physics) is the maximum rate at which information can propagate. It is therefore an upper bound to the speed at which any pattern can move.
A puffer whose debris consists entirely of spaceships is called a rake. The first known puffer, in Conway's Game of Life, was discovered by Bill Gosper; it is a dirty puffer, but eventually stabilizes to leave a pattern of debris that repeats every 140 generations. Since then, many puffers have been discovered for this cellular automaton, with many different speeds and periods. Puffers are significant for Life and related rules for three reasons: First, if they can be stabilized in such a way that they produce only gliders (that is, turned into rakes) they can be used as part of many more complex patterns such as breeders.
He also invented several well-known cellular automaton rules, including Brian's Brain, Seeds, and Wireworld. *.
SMM – A gun that fires out rakes. MSM – A puffer that leaves guns in its wake. MMS – A rake that fires out puffers. MMM – A rake that fires out more rakes, such that there are no stationary elements.
In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit", as the argument or sequence position goes to infinity – in big Theta notation, f(x) = Θ(x 2 ). This can be defined both continuously (for a real-valued function of a real variable) or discretely (for a sequence of real numbers, i.e., real-valued function of an integer or natural number variable).
neighbours8 connectivityinfluence its nearest neighbours
In cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells that surround it.
The glider is a pattern that travels across the board in Conway's Game of Life. It was first discovered by Richard K. Guy in 1970, while John Conway's group was attempting to track the evolution of the R-pentomino. Gliders are the smallest spaceships, and they travel diagonally at a speed of one cell every four generations, or c/4. The glider is often produced from randomly generated starting configurations. John Conway has remarked that he wishes he hadn't called it the glider. The game was developed before the widespread use of interactive computers, and after seeing it animated, he feels the glider looks more like an ant walking across the plane.
In a cellular automaton, a gun is a pattern with a main part that repeats periodically, like an oscillator, and that also periodically emits spaceships. There are then two periods that may be considered: the period of the spaceship output, and the period of the gun itself, which is necessarily a multiple of the spaceship output's period. A gun whose period is larger than the period of the output is a pseudoperiod gun.
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B are orthogonal when B(u, v) = 0. Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis.
Day & NightDay and Night'' (cellular automaton)
Day and Night is a cellular automaton rule in the same family as Game of Life. It is defined by rule notation B3678/S34678, meaning that a dead cell becomes live (is born) if it has 3, 6, 7, or 8 live neighbors, and a live cell remains alive (survives) if it has 3, 4, 6, 7, or 8 live neighbors, out of the eight neighbors in the Moore neighborhood. It was invented and named by Nathan Thompson in 1997, and investigated extensively by David I. Bell. The rule is given the name "Day & Night" because its on and off states are symmetric: if all the cells in the Universe are inverted, the future states are the inversions of the future states of the original pattern.
In a cellular automaton, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of generations. Thus the evolution of such a pattern repeats itself indefinitely. Depending on context, the term may also include spaceships as well.
Rake (train), a line of coupled passenger coaches, or freight wagons, or railcars (excluding the locomotive) that typically move together. Rake (angle), mathematical definition. Rake (cellular automaton), a cellular automaton pattern that moves while regularly emitting spaceships. Rake (poker), the commission taken by a casino when hosting a poker game. Rake (software), a variant of the make program coded in the Ruby programming language. A guitar-playing method involving muted notes. Rake (band), an American noise rock/avant-garde musical ensemble. Rake (Australian TV series), an Australian television series that commenced airing in 2010. Rake (U.S.