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Gemini is also a spaceship, and is the first spaceship constructed in the Game of Life that is an oblique spaceship, which is a spaceship that is neither orthogonal nor purely diagonal.
On November 23, , Dave Greene built the first replicator in the Game of Life that creates a complete copy of itself, including the instruction tape.
In October , Adam P. Goucher finished his construction of the 0E0P metacell, a metacell capable of self-replication.
This differed from previous metacells, such as the OTCA metapixel by Brice Due, which only worked with already constructed copies near them.
The 0E0P metacell works by using construction arms to create copies that simulate the programmed rule. From most random initial patterns of living cells on the grid, observers will find the population constantly changing as the generations tick by.
The patterns that emerge from the simple rules may be considered a form of mathematical beauty. Small isolated subpatterns with no initial symmetry tend to become symmetrical.
Once this happens, the symmetry may increase in richness, but it cannot be lost unless a nearby subpattern comes close enough to disturb it.
In a very few cases, the society eventually dies out, with all living cells vanishing, though this may not happen for a great many generations.
Most initial patterns eventually burn out, producing either stable figures or patterns that oscillate forever between two or more states;   many also produce one or more gliders or spaceships that travel indefinitely away from the initial location.
Because of the nearest-neighbour based rules, no information can travel through the grid at a greater rate than one cell per unit time, so this velocity is said to be the cellular automaton speed of light and denoted c.
Early patterns with unknown futures, such as the R-pentomino, led computer programmers to write programs to track the evolution of patterns in the Game of Life.
Most of the early algorithms were similar: they represented the patterns as two-dimensional arrays in computer memory. Typically, two arrays are used: one to hold the current generation, and one to calculate its successor.
Often 0 and 1 represent dead and live cells, respectively. A nested for loop considers each element of the current array in turn, counting the live neighbours of each cell to decide whether the corresponding element of the successor array should be 0 or 1.
The successor array is displayed. For the next iteration, the arrays swap roles so that the successor array in the last iteration becomes the current array in the next iteration.
A variety of minor enhancements to this basic scheme are possible, and there are many ways to save unnecessary computation. A cell that did not change at the last time step, and none of whose neighbours changed, is guaranteed not to change at the current time step as well, so a program that keeps track of which areas are active can save time by not updating inactive zones.
To avoid decisions and branches in the counting loop, the rules can be rearranged from an egocentric approach of the inner field regarding its neighbours to a scientific observer's viewpoint: if the sum of all nine fields in a given neighbourhood is three, the inner field state for the next generation will be life; if the all-field sum is four, the inner field retains its current state; and every other sum sets the inner field to death.
To save memory, the storage can be reduced to one array plus two line buffers. One line buffer is used to calculate the successor state for a line, then the second line buffer is used to calculate the successor state for the next line.
The first buffer is then written to its line and freed to hold the successor state for the third line. If a toroidal array is used, a third buffer is needed so that the original state of the first line in the array can be saved until the last line is computed.
In principle, the Game of Life field is infinite, but computers have finite memory. This leads to problems when the active area encroaches on the border of the array.
Programmers have used several strategies to address these problems. The simplest strategy is to assume that every cell outside the array is dead.
This is easy to program but leads to inaccurate results when the active area crosses the boundary. A more sophisticated trick is to consider the left and right edges of the field to be stitched together, and the top and bottom edges also, yielding a toroidal array.
The result is that active areas that move across a field edge reappear at the opposite edge. Inaccuracy can still result if the pattern grows too large, but there are no pathological edge effects.
Techniques of dynamic storage allocation may also be used, creating ever-larger arrays to hold growing patterns.
The Game of Life on a finite field is sometimes explicitly studied; some implementations, such as Golly , support a choice of the standard infinite field, a field infinite only in one dimension, or a finite field, with a choice of topologies such as a cylinder, a torus, or a Möbius strip.
Alternatively, programmers may abandon the notion of representing the Game of Life field with a two-dimensional array, and use a different data structure, such as a vector of coordinate pairs representing live cells.
This allows the pattern to move about the field unhindered, as long as the population does not exceed the size of the live-coordinate array.
The drawback is that counting live neighbours becomes a hash-table lookup or search operation, slowing down simulation speed. With more sophisticated data structures this problem can also be largely solved.
For exploring large patterns at great time depths, sophisticated algorithms such as Hashlife may be useful.
There is also a method for implementation of the Game of Life and other cellular automata using arbitrary asynchronous updates whilst still exactly emulating the behaviour of the synchronous game.
Since the Game of Life's inception, new, similar cellular automata have been developed. A cell is born if it has exactly three neighbours, survives if it has two or three living neighbours, and dies otherwise.
The first number, or list of numbers, is what is required for a dead cell to be born. The second set is the requirement for a live cell to survive to the next generation.
Cellular automata on a two-dimensional grid that can be described in this way are known as Life-like cellular automata. HighLife is best known for its frequently occurring replicators.
Additional Life-like cellular automata exist. The vast majority of these 2 18 different rules  produce universes that are either too chaotic or too desolate to be of interest, but a large subset do display interesting behavior.
A further generalization produces the isotropic rulespace, with 2 possible cellular automaton rules  the Game of Life again being one of them.
These are rules that use the same square grid as the Life-like rules and the same eight-cell neighbourhood, and are likewise invariant under rotation and reflection.
However, in isotropic rules, the positions of neighbour cells relative to each other may be taken into account in determining a cell's future state—not just the total number of those neighbours.
Some variations on the Game of Life modify the geometry of the universe as well as the rule. The above variations can be thought of as a two-dimensional square, because the world is two-dimensional and laid out in a square grid.
One-dimensional square variations, known as elementary cellular automata ,  and three-dimensional square variations have been developed, as have two-dimensional hexagonal and triangular variations.
A variant using aperiodic tiling grids has also been made. Conway's rules may also be generalized such that instead of two states, live and dead , there are three or more.
State transitions are then determined either by a weighting system or by a table specifying separate transition rules for each state; for example, Mirek's Cellebration 's multi-coloured Rules Table and Weighted Life rule families each include sample rules equivalent to the Game of Life.
Patterns relating to fractals and fractal systems may also be observed in certain Life-like variations. Immigration is a variation that is very similar to the Game of Life, except that there are two on states, often expressed as two different colours.
Whenever a new cell is born, it takes on the on state that is the majority in the three cells that gave it birth.
This feature can be used to examine interactions between spaceships and other objects within the game.
When a new cell is born from three different on neighbours, it takes the fourth value, and otherwise, like Immigration, it takes the majority value.
Computers have been used to follow Game of Life configurations since it was first publicized. When John Conway was first investigating how various starting configurations developed, he tracked them by hand using a go board with its black and white stones.
This was tedious and prone to errors. This program showed that the configuration had not reached a stable state after 1, generations.
Guy and S. The results were published in the October issue of Scientific American , along with the statement: "Without its help, some discoveries about the game would have been difficult to make.
The first was in the January issue of Acorn User magazine, and Banthorpe followed this with a three-dimensional version in the May issue.
There are now thousands of Game of Life programs online, so a full list will not be provided here. The following is a small selection of programs with some special claim to notability, such as popularity or unusual features.
Most of these programs incorporate a graphical user interface for pattern editing and simulation, the capability for simulating multiple rules including the Game of Life, and a large library of interesting patterns in the Game of Life and other cellular automaton rules.
Google implemented an easter egg of the Game of Life in Users who search for the term are shown an implementation of the game in the search results page.
From Wikipedia, the free encyclopedia. Two-dimensional cellular automaton devised by J. Conway in For Conway's surreal number game theory, see Surreal number.
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Unreliable citations may be challenged or deleted. July Learn how and when to remove this template message. A single Gosper 's glider gun creating gliders.
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