John von Neumann has defined life (despite his careful disclaimers) in late 1940 as a creation (being or organism) which:
John von Neumann was thinking about an engineering solution which would use electromagnetic components floating randomly in liquid (or gas). This turned out not to be realistic at the given technology state of those days. Thus, ingeniously, Stanisław Ulam invented the cell automata which in principle were supposed to simulate von Neumann's potential electro-magnetic constructions. Ulam discussed his cell automata in 2-dimensional lattice, in several papers; he applied the early computers to do so. In parallel, John von Neumann attempted to construct Ulam's cellular automaton. He virtually succeeded. He was busy with his other projects, thus, he left some details unfinished. His construction was complicated because it tried to simulate his own engineering design. Over time, simpler life constructions were provided by other researchers, and published in papers and books.
The initial goal of John Conway was to define an interesting and unpredictable cell automaton. Thus, he wanted some configurations to last for a long time before dying, other configurations to go on forever without allowing cycles, etc. It was a significant challenge and an open problem for years before experts on cell automatons managed to prove that indeed, Conway' LIFE game admitted a configuration which was *alive* in the sense of satisfying the two John von Neumann's general axioms of life, mentioned above.
While the definitions before Conway's LIFE were proof-oriented, Conway's construction simply aimed at simplicity without a priori aiming at the proof of automaton being alive.
The game made its first public appearance in the October 1970 issue of Scientific American, in Martin Gardner's "Mathematical Games" column. From a theoretical point of view, it is interesting because it has the power of a universal Turing machine: that is, anything that can be computed algorithmically can be computed within Conway's Game of Life. Gardner wrote:
The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata ... Because of Life's analogies with the rise, fall and alterations of a society of living organisms, it belongs to a growing class of what are called "simulation games" (games that resemble real life processes).
Ever since its publication, Conway's Game of Life has attracted much interest, because of the surprising ways in which the patterns can evolve. Life provides an example of emergence and self-organization. Scholars in various fields, such as computer science, physics, biology, biochemistry, economics, mathematics, philosophy, and generative sciences have made use of the way that complex patterns can emerge from the implementation of the game's simple rules. The game can also serve as a didactic analogy, used to convey the somewhat counterintuitive notion that "design" and "organization" can spontaneously emerge in the absence of a designer. For example, philosopher and cognitive scientist Daniel Dennett has used the analogy of Conway's Life "universe" extensively to illustrate the possible evolution of complex philosophical constructs, such as consciousness and free will, from the relatively simple set of deterministic physical laws, which might govern our universe.
The popularity of Conway's Game of Life was helped by its coming into being just in time for a new generation of inexpensive computer access which was being released into the market. The game could be run for hours on these machines, which would otherwise have remained unused at night. In this respect, it foreshadowed the later popularity of computer-generated fractals. For many, Life was simply a programming challenge: a fun way to use otherwise wasted CPU cycles. For some, however, Life had more philosophical connotations. It developed a cult following through the 1970s and beyond; current developments have gone so far as to create theoretic emulations of computer systems within the confines of a Life board.
Conway chose his rules carefully, after considerable experimentation, to meet these criteria:
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.
It can be asked whether Life is decidable: whether an algorithm exists, so that given an "initial" pattern and a "later" pattern, the algorithm can tell whether, starting with the initial pattern, the later pattern is ever going to appear. This turns out to be impossible: no such algorithm exists. This is in fact a corollary of the halting problem.
Indeed, since Life includes a pattern that is equivalent to a UTM (universal Turing machine), this "deciding" algorithm, if it existed, could have been used to solve the halting problem, by taking the initial pattern as the one corresponding to a UTM+input and the later pattern as the one corresponding to a halting state of the machine with an empty tape (as one can modify the Turing machine to always erase the tape before halting). However the halting problem is provably undecidable and so such an algorithm does not exist.
It also follows that some patterns exist that remain chaotic forever: otherwise one could progress the game sequentially until a non-chaotic pattern emerges, and then compute whether a later pattern is going to appear.
On May 18, 2010, Andrew J. Wade announced a self-constructing pattern dubbed Gemini which creates a copy of itself while destroying its parent. This pattern replicates in 34 million generations, and uses an instruction tape made of gliders which oscillate between two stable configurations made of Chapman-Greene construction arms. 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 a knightship, 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 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 across the world to write programs to track the evolution of Life patterns. Most of the early algorithms were similar; they represented Life patterns as two-dimensional arrays in computer memory. Typically two arrays are used, one to hold the current generation, and one in which 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 the 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 is 3, the inner field state for the next generation will be life (no matter of its previous contents); if the all-field sum is 4, the inner field retains its current state and every other sum sets the inner field to death.
If it is desired to save memory, the storage can be reduced to one array plus 3 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 at least 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, like 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.
HOPE YOU'VE ENJOYED!!
Written by Rick Brown 2018 - All text taken from Wikipedia