A269813 First differences of 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.

3, 1, 27, -23, 83, -71, 143, -139, 263, -251, 383, -363, 515, -487, 647, -643, 895, -883, 1143, -1123, 1399, -1355, 1607, -1563, 1875, -1815, 2143, -2131, 2467, -2399, 2735, -2731, 3239, -3227, 3743, -3723, 4255, -4211, 4719, -4675, 5239, -5163, 5711, -5659

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

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 *)
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. A269810.

Sequence in context: A271203 A271151 A027495 * A271128 A271163 A270017

Adjacent sequences: A269810 A269811 A269812 * A269814 A269815 A269816

Keyword

sign,easy

Author

Robert Price, Mar 05 2016

Status

approved