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A271249 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 315", based on the 5-celled von Neumann neighborhood. 1
4, 4, 23, -19, 91, -79, 167, -139, 271, -259, 360, -304, 488, -489, 725, -744, 1035, -1031, 1260, -1133, 1389, -1409, 1833, -1797, 2049, -1917, 2289, -2136, 2499, -2487, 2988, -2960, 3395, -3347, 3935, -3831, 4215, -4135, 4663, -4507, 5123, -4983, 5507 (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=315; 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. A266206.

Sequence in context: A271457 A268194 A271408 * A271167 A271155 A271132

Adjacent sequences:  A271246 A271247 A271248 * A271250 A271251 A271252

KEYWORD

sign,easy

AUTHOR

Robert Price, Apr 02 2016

STATUS

approved

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Last modified October 28 07:30 EDT 2021. Contains 348320 sequences. (Running on oeis4.)