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7845110
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2011-10-21T04:54:43.383
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2011-10-21T04:54:43.383
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To be clear (because your ^ symbols were missing), you are asking: <blockquote> Given a square of 2^(2k) cells, 2^k on a side, at the kth level of the tree, the hash table stores the 2^(k-1)-by-2^(k-1) square of cells in the center, 2^(k-2) generations in the future. [...] So given a 8x8 initial configuration [...] With every new generation our view of the grid reduces, in-turn we get the next state of the automata. We canot go any further after getting the inner most 2x2 square 2^k-2 generations forward. So how does the hashlife in Golly go on forever? Also its view of the field never seems to reduce. </blockquote> Instead of starting with your 8x8 pattern, imagine instead that you start with a bigger pattern that happens to contain your 8x8 pattern inside it. For example, you could start with a 16x16 pattern that has your 8x8 pattern in the center, and a 4-row margin of blank cells all around the edges. Such a pattern is easy to construct, by assembling blank 4x4 nodes with the 4x4 subnodes of your 8x8 start pattern. Given such a 16x16 pattern, the HashLife algorithm can give you an 8x8 answer, 4 generations in the future. You want more? Okay, start with a 32x32 pattern that contains mostly blank space, with the 8x8 pattern in the center. With this you can get a 16x16 answer that is 8 generations into the future. What if your pattern contains moving objects that move fast enough that they go outside that 16x16 area after 8 generations? Simple -- start with a 64x64 start pattern, but instead of trying to run it for a whole 16 generations, just run it for 8 generations. In general, all cases of arbitrarily large, possibly expanding patterns, over arbitrarily long periods of time, can be handled (and in fact are handled in Golly) by adding as much blank space as needed around the outside of the pattern.
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1. POHow does the hashlife alg go on forever in Golly?
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1. PTAnswer
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1. USRobert Munafo
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