And ‘off’ cell (t -1) with exactly three ‘on’ neighbours (t -1) transitions to an ‘on’ state at time t.Any ‘on’ cell (t -1) with more than three ‘on’ neighbours (t -1) transitions to an ‘off’ state at time t.Any ‘on’ cell (t -1) with two or three ‘on’ neighbours (t -1) remains ‘on’ at time t.Any ‘on’ cell (at time t-1) with fewer than two ‘on’ neighbours (at t -1) transitions to an ‘off’ state at time t.The game takes place in discrete time, with the state of each cell at time t determined by its own state and the states of its eight immediate neighbours at t-1 (the Moore neighbourhood of radius 1), according to the following simple rules: In its standard format, the Game of Life unfolds on an infinite two-dimensional grid composed of cells each of which is either ‘on/alive’ or ‘off/dead’. 5 Implications: Emergence, self-organization, autopoeisis, and the physics of information. Even though its (simple) rules are specified at the level of individual cells, one sees entities at coarse-grained ‘higher’ levels of description, whose behaviors are better described by rules at these higher levels. One reason for its appeal is that it is very simple to program, yet at the same time it appears to exemplify emergent and self-organized behaviour. First popularized in 1970 in the Scientific American (Gardner, 1970), the Game of Life has attracted lasting appeal among both scientific and amateur communities. Following specification of an initial configuration, patterns evolve over time across the grid requiring no further user input (thus ‘zero-player’). It takes place on an infinite two-dimensional grid in which cells can be ‘on’ (alive) or ‘off’ (dead), and is defined by a set of rules that jointly determine the state of a cell given the state of its neighbours. The Game of Life (sometimes known simply as Life) is an example of a cellular automaton and a zero-player game. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopediaĭr. I've tested it and they do seem to consistently remember the exact state of the simulation at least a few levels up - it's easy to check by looking at the length of the clock train on the left of the metapixel in each level.Eugene M. I suppose this means that if you zoom out a lot (just spam the scroll) and then zoom in a lot, there might be substantial memory usage. The only problem is that you do have to store state for levels between the highest level you've seen and the current level as you zoom in. I suspect the trick is to only store the state for any levels you've actually seen.Īs you go higher, they can just arbitrarily select a location in the simulation a few levels up from where you are that is consistent with the metapixels you've seen once you go up a few levels, there's no chance of you having seen beyond a very small window of the simulation, so it's a matter of just finding a matching pattern.Īs you go lower, the time step cannot be set be zero, so they can simply initialize the simulation a few levels down to an arbitrary state since the lower levels will tick exponentially faster. Yeah, this part is very clever and quite well-done IMHO. Based on the current state (on or off), a series of "glider guns" will be conditionally activated, which creates the appearance of a filled center (filled with moving gliders). It's fun to zoom in on the posted site and identify all the features, like the rule table near the bottom left.įor context, the OTCA metapixel is a large pattern (2048x2048) which is capable of simulating Conway's Game of Life rules (or, indeed, any rule set consisting of neighbour-counting birth/death conditions) it does this by having adjacent pixels coordinate sharing of state (whether they're on or off) and then looking up what to do via a (programmable) lookup table. There's some lovely "engineering diagrams" of the OTCA metapixel on this (sparse) blog. The other trick is that the simulation speed scales with draw distance, such that once you've zoomed out a full cycle the simulation has gotten exactly 35328x faster, which is the period of the OTCA metapixel.
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