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Search: id:A151725
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| A151725 |
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Number of ON states after n generations of cellular automaton based on square grid with each cell adjacent to its eight neighbors. |
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+0
11
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| 0, 1, 9, 13, 33, 37, 57, 77, 121, 125, 145, 165, 209, 237, 297, 373, 465, 469, 489, 509, 553, 581, 641, 717, 809, 837, 897, 981, 1097, 1213, 1409, 1645, 1833, 1837, 1857, 1877, 1921, 1949, 2009, 2085, 2177, 2205, 2265, 2349, 2465, 2581, 2777, 3013
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A cell is turned ON if exactly one of its eight neighbors is ON. An ON cell remains ON for ever.
We start with a single ON cell.
Analog of A147562, which is the case when each cell has only four neighbors.
The equivalent Mathematica cellular automaton is obtained with neighborhood weights {{1,1,1},{1,9,1},{1,1,1}}, rule number 261634, and starting configuration {{1}}. [From John W. Layman (layman(AT)math.vt.edu), Sep 11 2009]
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LINKS
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David Applegate, Table of n, a(n) for n = 0..1000
David Applegate, The movie version
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MATHEMATICA
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RasterGraphics[state_?MatrixQ, colors_Integer : 2, opts___] := Graphics[Raster[ Reverse[1 - state/(colors - 1)]], AspectRatio -> (AspectRatio /. {opts} /. AspectRatio -> Automatic), Frame -> True, FrameTicks -> None, GridLines -> None]; wt = {{1, 1, 1}, {1, 9, 1}, {1, 1, 1}}; rule= 261634; init={{1}}; Show[GraphicsArray[Map[RasterGraphics, CellularAutomaton[{rule, {2, wt}, {1, 1}}, {init, 0}, 9, -10]]]]; nx = 100; ca = CellularAutomaton[{rule, {2, wt}, {1, 1}}, {init, 0}, nx - 1, -nx]; a = Table[Total[ca[[i]], 2], {i, 1, nx}] [From John W. Layman (layman(AT)math.vt.edu), Sep 11 2009]
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CROSSREFS
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Cf. A151726, A147562, A147582, A151723, A151735.
See A151731, A151732, A151733, A151734 for the same CA except that two neighbors must be ON for a cell to turn ON.
Sequence in context: A098074 A032361 A031196 this_sequence A146864 A146739 A146723
Adjacent sequences: A151722 A151723 A151724 this_sequence A151726 A151727 A151728
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KEYWORD
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nonn
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AUTHOR
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David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2009
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