solved. For exploring large patterns at great time depths, sophisticated algorithms such as Hashlife may be useful. There is also a method for implementation of the Game of Life and other cellular automata using arbitrary asynchronous updates whilst still exactly emulating the behaviour of the synchronous game. Source code examples that implement the basic Game of Life scenario in various programming languages, including C, C++, Java and Python can be found at Rosetta Code. Variations Since the Game of Life's inception, new, similar cellular automata have been developed. The standard Game of Life is symbolized in rule-string notation as B3/S23. A cell is born if it has exactly three neighbours, survives 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. Hence B6/S16 means "a cell is born if there are six neighbours, and lives on if there are either one or six neighbours". Cellular automata on a two-dimensional grid that can be described in this way are known as cellular automata. Another common automaton, Highlife, is described by the rule B36/S23, because having six neighbours, in addition to the original game's B3/S23 rule, causes a birth. HighLife is best known for its frequently occurring replicators. Additional Life-like cellular automata exist. The vast majority of these 218 different rules produce universes that are either too chaotic or too desolate to be of interest, but a large subset do display interesting behavior. A further generalization produces the isotropic rulespace, with 2102 possible cellular automaton rules (the Game of Life again being one of them). These are rules that use the same square grid as the Life-like rules and the same eight-cell neighbourhood, and are likewise invariant under rotation and reflection. However, in isotropic rules, the positions of neighbour cells relative to each other may be taken into account in determining a cell's future state—not just the total number of those neighbours. Some variations on the Game of Life modify the geometry of the universe as well as the rule. The above variations can be thought of as a two-dimensional square, because the world is two-dimensional and laid out in a square grid. One-dimensional square variations, known as elementary cellular automata, and three-dimensional square variations have been