A271121 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 286", based on the 5-celled von Neumann neighborhood.

1, 5, 12, 17, 37, 28, 76, 45, 112, 72, 153, 121, 204, 145, 301, 196, 344, 277, 404, 360, 497, 372, 632, 489, 740, 536, 849, 681, 1008, 672, 1141, 893, 1248, 940, 1473, 1101, 1592, 1180, 1741, 1405, 1924, 1468, 2121, 1637, 2356, 1728, 2513, 2013, 2748, 2072

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=286; 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: A063297 A237669 A022137 * A271301 A282696 A314288

Adjacent sequences: A271118 A271119 A271120 * A271122 A271123 A271124

Keyword

nonn,easy

Author

Robert Price, Mar 31 2016

Status

approved