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A272581 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 505", based on the 5-celled von Neumann neighborhood. 4
1, 4, 13, 40, 29, 100, 69, 200, 85, 324, 133, 480, 181, 644, 309, 872, 325, 1124, 373, 1408, 421, 1700, 565, 2048, 613, 2404, 757, 2792, 901, 3140, 1301, 3624, 1317, 4132, 1365, 4672, 1413, 5220, 1557, 5824, 1605, 6436, 1749, 7080, 1893, 7684, 2325, 8416 (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=505; 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: A133409 A000746 A271012 * A191132 A119915 A137744

Adjacent sequences:  A272578 A272579 A272580 * A272582 A272583 A272584

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 03 2016

STATUS

approved

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Last modified November 14 06:14 EST 2018. Contains 317162 sequences. (Running on oeis4.)