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A273270 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 625", based on the 5-celled von Neumann neighborhood. 4
1, 4, 21, 29, 72, 84, 141, 168, 260, 289, 369, 384, 528, 564, 684, 728, 948, 976, 1164, 1232, 1412, 1416, 1597, 1705, 2064, 2113, 2361, 2316, 2688, 2776, 3013, 2989, 3492, 3593, 3869, 4117, 4453, 4484, 4793, 4869, 5329, 5516, 6009, 5941, 6408, 6424, 7012 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Initialized with a single black (ON) cell at stage zero.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

LINKS

Robert Price, Table of n, a(n) for n = 0..128

Robert Price, Diagrams of the first 20 stages

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=625; stages=128;

rule=IntegerDigits[code, 2, 10];

g=2*stages+1; (* Maximum size of grid *)

a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)

ca=a;

ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];

PrependTo[ca, a];

(* Trim full grid to reflect growth by one cell at each stage *)

k=(Length[ca[[1]]]+1)/2;

ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];

Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

CROSSREFS

Sequence in context: A304770 A316513 A273208 * A273246 A273299 A306285

Adjacent sequences: A273267 A273268 A273269 * A273271 A273272 A273273

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 18 2016

STATUS

approved

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Last modified December 4 23:46 EST 2022. Contains 358572 sequences. (Running on oeis4.)