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A271098 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 278", based on the 5-celled von Neumann neighborhood. 1
4, 3, 12, -4, 28, -12, 56, -44, 88, -72, 136, -107, 168, -157, 232, -167, 260, -265, 352, -263, 388, -405, 488, -375, 580, -593, 664, -531, 768, -805, 848, -716, 952, -956, 1100, -1000, 1208, -1167, 1356, -1249, 1484, -1464, 1628, -1471, 1792, -1765, 2020 (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

Robert Price, Table of n, a(n) for n = 0..127

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=278; 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. A271095.

Sequence in context: A204291 A270324 A271888 * A269718 A099377 A121844

Adjacent sequences:  A271095 A271096 A271097 * A271099 A271100 A271101

KEYWORD

sign,easy

AUTHOR

Robert Price, Mar 30 2016

STATUS

approved

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Last modified October 22 17:33 EDT 2019. Contains 328319 sequences. (Running on oeis4.)