Supports very high-period and slow spaceships. Named after Stephen Morley also called Move. Has engineered patterns with highly complex behavior. Similar to Life but with a small self-replicating pattern. Has complex oscillators of high periods as well as a small glider. If a pattern is composed of 2x2 blocks, it will continue to evolve in the same form grouping these blocks into larger powers of two leads to the same behavior, but slower. First studied by Dean Hickerson, who in 1993 offered a $50 prize to find a pattern that fills space with live cells the prize was won in 1999 by David Bell. įorms large diamonds with chaotically fluctuating boundaries. Has many small oscillators and spaceships. Was initially thought to be a stable alternative to Life, until computer simulation found that larger patterns tend to explode. It combines chaotic growth with more structured ladder-like patterns that can be used to simulate arbitrary Boolean circuits. This rule supports a small self-replicating pattern which, when combined with a small glider pattern, causes the glider to bounce back and forth in a pseudorandom walk. However, some engineered patterns with complex behavior are known. Īll patterns are phoenixes, meaning that every live cell immediately dies, and many patterns lead to explosive chaotic growth. In the descriptions below, all rules are specified in Golly/RLE format.Įdward Fredkin's replicating automaton: every pattern is eventually replaced by multiple copies of itself. There are 2 18 = 262,144 possible Life-like rules, only a small fraction of which have been studied in any detail. The "B" in this format stands for "birth" and the "S" stands for "survival". Thus, in this notation, Conway's Game of Life is denoted B3/S23.
In the notation used by the Golly open-source cellular automaton package and in the RLE format for storing cellular automaton patterns, a rule is written in the form By/Sx where x and y are the same as in the MCell notation. For instance, in this notation, Conway's Game of Life is denoted 23/3. The presence of a digit d in the x string means that a live cell with d live neighbors survives into the next generation of the pattern, and the presence of d in the y string means that a dead cell with d live neighbors becomes alive in the next generation. In the notation used by Mirek's Cellebration, a rule is written as a string x/y where each of x and y is a sequence of distinct digits from 0 to 8, in numerical order. The other two notations unpack the same sequence of bits into a string of characters that is more easily read by a human. Wolfram & Packard (1985) use the Wolfram code, a decimal number the binary representation of which has bits that correspond to each possible number of neighbors and state of a cell the bits of this number are zero or one accordingly as a cell with that neighborhood is dead or alive in the next generation. There are three standard notations for describing these rules, that are similar to each other but incompatible. It is common to refer to it as the "Life family" or to simply use phrases like "similar to Life". Many different terms are used to describe this class. This class of cellular automata is named for the Game of Life (B3/S23), the most famous cellular automaton, which meets all of these criteria. In each time step of the automaton, the new state of a cell can be expressed as a function of the number of adjacent cells that are in the alive state and of the cell's own state that is, the rule is outer totalistic (sometimes called semitotalistic).The neighborhood of each cell is the Moore neighborhood it consists of the eight adjacent cells to the one under consideration and (possibly) the cell itself.Each cell of the automaton has two states (conventionally referred to as "alive" and "dead", or alternatively "on" and "off").The array of cells of the automaton has two dimensions.Type of cellular automaton with similarities to Conway's Game of LifeĪ cellular automaton (CA) is Life-like (in the sense of being similar to Conway's Game of Life) if it meets the following criteria:
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