A269810 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 33", based on the 5-celled von Neumann neighborhood.

1, 4, 5, 32, 9, 92, 21, 164, 25, 288, 37, 420, 57, 572, 85, 732, 89, 984, 101, 1244, 121, 1520, 165, 1772, 209, 2084, 269, 2412, 281, 2748, 349, 3084, 353, 3592, 365, 4108, 385, 4640, 429, 5148, 473, 5712, 549, 6260, 601, 6784, 741, 7308, 753, 7940, 877

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

rule=33; stages=300;
ca=CellularAutomaton[{rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *)
l=Length[ca[[1]]]; k=(l+1)/2; s=stages; (* Limit scope to one cell growth per stage *)
ca=Table[Table[Part[ca[[n]][[j]], Range[Max[1, k+1-n], Min[l, k-1+n]]], {j, Max[1, k+1-n], Min[l, k-1+n]}], {n, 1, s+1}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Crossrefs

Sequence in context: A326998 A270286 A271803 * A271125 A270014 A271160

Adjacent sequences: A269807 A269808 A269809 * A269811 A269812 A269813

Keyword

nonn,easy

Author

Robert Price, Mar 05 2016

Status

approved