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A273491 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 758", based on the 5-celled von Neumann neighborhood. 0
4, 4, 12, 12, 12, 16, 24, 44, 28, 32, 32, 60, 28, 48, 56, 76, 60, 64, 64, 92, 60, 80, 80, 108, 76, 96, 80, 124, 60, 112, 120, 140, 124, 128, 128, 156, 124, 144, 144, 172, 140, 160, 144, 188, 124, 176, 176, 204, 172, 192, 176, 220, 156, 208, 192, 236, 172 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Table of n, a(n) for n=0..56.

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=758; 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}];

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

Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

CROSSREFS

Cf. A273486.

Sequence in context: A241496 A273412 A206488 * A168398 A281913 A178776

Adjacent sequences:  A273488 A273489 A273490 * A273492 A273493 A273494

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 23 2016

STATUS

approved

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Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)