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Furthermore, a pattern can contain a collection of guns that fire gliders in such a way as to construct new objects, including copies of the original pattern.
A universal constructor can be built which contains a Turing complete computer, and which can build many types of complex objects, including more copies of itself.
This is the first new spaceship movement pattern for an elementary spaceship found in forty-eight years. Many patterns in the Game of Life eventually become a combination of still lifes, oscillators, and spaceships; other patterns may be called chaotic.
A pattern may stay chaotic for a very long time until it eventually settles to such a combination. Life is undecidable , which means that given an initial pattern and a later pattern, no such algorithm exists that can tell whether the later pattern is ever going to appear.
This is a corollary of the halting problem: Indeed, since Life includes a pattern that is equivalent to a Universal Turing Machine UTM , this deciding algorithm, if it existed, could be used to solve the halting problem by taking the initial pattern as the one corresponding to a UTM plus an input, and the later pattern as the one corresponding to a halting state of the UTM.
It also follows that some patterns exist that remain chaotic forever. If this were not the case, one could progress the game sequentially until a non-chaotic pattern emerged, then compute whether a later pattern was going to appear.
On May 18, , Andrew J. Wade announced a self-constructing pattern, dubbed "Gemini", that creates a copy of itself while destroying its parent.
These, in turn, create new copies of the pattern, and destroy the previous copy. 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.
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 sub patterns 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 sub pattern 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 across the world to write programs to track the evolution of Life patterns.
Most of the early algorithms were similar: Typically two arrays are used: 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. If it is desired 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 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.
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.
Patterns relating to fractals and fractal systems may also be observed in certain Life -like variations. 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.
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. 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 It was created and co-designed by toy and game designer Reuben Klamer  and was "heartily endorsed" by Art Linkletter.
The game was originally created in by Milton Bradley as The Checkered Game of Life , and was the first game created by Bradley, a successful lithographer.
His most important product to that point had been a portrait of Abraham Lincoln with a clean-shaven face, which did not do well once Lincoln grew his famous beard.
The game sold 45, copies by the end of its first year. Like many 19th-century games, such as The Mansion of Happiness by S.
Ives in , it had a strong moral message. The game board resembled a modified checkerboard. The object was to land on "good" spaces and collect points.
A player could gain 50 points by reaching "Happy Old Age" in the upper-right corner, opposite "Infancy" where one began. In the modern version, The Game of Life , was introduced.
A collaboration between Reuben Klamer and Bill Markham, it consists of a track which passes along, over, and through small mountains , buildings, and other features.
A player travels along the track in a small plastic automobile, according to the spins of a small wheel on the board with spaces numbered 1 through Each car has six holes into which pegs are added as the player "gets married" and "acquires children".
Some "early modern" editions have eight cars. Other tangibles vary between versions of the game. The Game of Life , copyrighted by the Milton Bradley Company in , had some differences from later versions.
For example, once a player reached the "Day of Reckoning", they had to choose between moving on to "Millionaire Acres" if they had a lot of money , or trying to become a "Millionaire Tycoon" if they had little or no money with the risk of being sent to the "Poor Farm".
About halfway through the production of this version, many dollar values doubled. This description focuses on the later version with the larger dollar amounts.
The late s version also replaced the convertibles from earlier versions with minivans. Early s-era convertibles were still used in the edition.
The "Poor Farm" is not present in this edition; however, players who were risking their cash or car if they were penniless on being a "Millionaire Tycoon" still ran the risk of losing all their cash and sitting out the rest of the game at Bankrupt if the number they bet on the strip does not show up when the wheel stops spinning.
The gold "Revenge" squares added a byline, "Sue for damages", in the edition.