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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 it is desired to save memory, the storage can be reduced to one array plus three 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 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 simply 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.
Alternatively, the programmer may abandon the notion of representing the Life field with a 2-dimensional array, and use a different data structure, such as a vector of coordinate pairs representing live cells.
This approach 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, applicable to other cellular automata too, for implementation of the Game of Life using arbitrary asynchronous updates whilst still exactly emulating the behaviour of the synchronous game.
Since Life ' s inception, new, similar cellular automata have been developed. A cell is B orn if it has exactly three neighbours, S urvives 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.
Some variations on Life modify the geometry of the universe as well as the rule. The above variations can be thought of as 2-D square, because the world is two-dimensional and laid out in a square grid.
A variant using non-periodic tile 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 Conway's 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 Conway's 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 on the fourth value, and otherwise, like Immigration , it takes the majority value.
Computers have been used to follow 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. The results were published in the October issue of Scientific American , along with the statement: There are now thousands 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 Life, and a large library of interesting patterns in Life and other CA rules.
Google implemented an easter egg of Conway's 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. For other uses, see Game of Life disambiguation. For Conway's surreal number game theory, see surreal number.
A single Gosper 's glider gun creating " gliders ". A sample of a step oscillator along with a 2-step oscillator and a 4-step oscillator from a 2-D hexagonal Game of Life rule H: Archived from the original on A New Kind of Science.
Paul Chapman 11 November Retrieved 12 July Winning Ways for your Mathematical Plays 2nd ed. A K Peters Ltd. Evolution and the Meanings of Life.
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Play this great sequel, where fresh features and boards of combined play makes the game feel brand new again! Live out the most exciting years in the life of Joan of Arc, the ultimate female warrior, in the ultimate epic battles!
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