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A164936
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Population in generation n of the following pattern in Conway's Game of Life: 00000010 00001011 00001010 00001000 00100000 10100000, where "1" is a live cell and "0" is a dead cell, and spaces indicate a line break.
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1
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10, 14, 13, 19, 16, 21, 20, 26, 24, 28, 30, 26, 34, 32, 29, 36, 22, 19, 18, 19, 21, 22, 26, 27, 38, 38, 46, 52, 54, 55, 58, 58, 51, 63, 38, 43, 36, 38, 41, 42, 39, 38, 36, 42, 47, 58, 60, 56, 55, 53, 60, 57, 62, 51, 49, 59, 45, 36, 34, 35, 35, 39, 36, 35, 36
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OFFSET
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0,1
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COMMENTS
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Because the pattern never stabilizes, the sequence will continue to grow. With 10 cells in its initial state, this is the smallest pattern that grows indefinitely in Conway's Game of Life.
Because this pattern evolves into a block-laying switch engine, some blinkers, a glider and some still lifes, the first differences of this sequence eventually (i.e., after about 600 generations) has period 288. - Nathaniel Johnston, May 15 2011
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LINKS
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FORMULA
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For n >= 708, a(n) = a(n-144) + 16. Hence, a(n) ~ n/9. - Eric M. Schmidt, Mar 10 2013
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EXAMPLE
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The pattern laid out graphically:
00000010
00001011
00001010
00001000
00100000
10100000
After 25 generations the population is 38, so a(25)=38.
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MATHEMATICA
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a[n_] :=
Total[CellularAutomaton[{224, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2,
2}}}, {1,
1}}, {{{0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 1, 1}, {0, 0,
0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0,
0, 0}, {1, 0, 1, 0, 0, 0, 0, 0}}, {{0}}}, {{n}}], Infinity]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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