The game can also serve as a didactic analogy, used to convey the somewhat counter-intuitive notion that design and organization can spontaneously emerge in the absence of a designer.  Gardner wrote, "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). Any live cell with two or three live neighbours survives. In principle, the Game of Life field is infinite, but computers have finite memory. For example, he wanted some configurations to last for a long time before dying and other configurations to go on forever without allowing cycles. , Since the Game of Life's inception, new, similar cellular automata have been developed. His construction was complicated because it tried to simulate his own engineering design.  In fact, several different programmable computer architectures have been implemented in the Game of Life, including a pattern that simulates Tetris. The drawback is that counting live neighbours becomes a hash-table lookup or search operation, slowing down simulation speed. Period refers to the number of ticks a pattern must iterate through before returning to its initial configuration. The first two create a single block-laying switch engine: a configuration that leaves behind two-by-two still life blocks as its translates itself across the game's universe. Von Neumann was thinking about an engineering solution which would use electromagnetic components floating randomly in liquid or gas. Frequently occurring examples (in that they emerge frequently from a random starting configuration of cells) of the three aforementioned pattern types are shown below, with live cells shown in black and dead cells in white. All three of the patterns shown below grow indefinitely. , 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. Ulam discussed using c… , On November 23, 2013, Dave Greene built the first replicator in the Game of Life that creates a complete copy of itself, including the instruction tape. Many different types of patterns occur in the Game of Life, which are classified according to their behaviour. For example, philosopher Daniel Dennett has used the analogy of the Game of 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. If a cell is OFF, and exactly 3 of its neighbors are ON, the cell turns ON in the next generation.  The name 0E0P is short for "Zero Encoded by Zero Population", which indicates that instead of a metacell being in an "off" state simulating empty space, the 0E0P metacell removes itself when the cell enters that state, leaving a blank space.. It can handle cellular automaton rules with the same neighbourhood as the Game of Life, and up to eight possible states per cell. If three gliders are shot in just the right way, the block will move farther away. 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. This turned out not to be realistic with the technology available at the time. Additional Life-like cellular automata exist.  Susan Stepney, Professor of Computer Science at the University of York, followed this up in 1988 with Life on the Line, a program that generated one-dimensional cellular automata.. Any live cell with two or three live neighbours lives on to the next generation. This has the same computational power as a universal Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints; it is Turing complete. , Conway originally conjectured that no pattern can grow indefinitely—i.e. Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. 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. Indeed, since the Game of 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. , In October 2018, Adam P. Goucher finished his construction of the 0E0P metacell, a metacell capable of self-replication.
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