A269817 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 35", based on the 5-celled von Neumann neighborhood.

4, 0, 32, -28, 92, -80, 164, -156, 284, -272, 416, -388, 560, -528, 716, -700, 956, -944, 1216, -1188, 1484, -1432, 1728, -1676, 2024, -1976, 2332, -2260, 2648, -2576, 2972, -2940, 3452, -3440, 3968, -3940, 4492, -4440, 4992, -4940, 5540, -5472, 6064, -5956

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=35; 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. A269814.

Sequence in context: A271256 A271057 A269879 * A270021 A270328 A270933

Adjacent sequences: A269814 A269815 A269816 * A269818 A269819 A269820

Keyword

sign,easy

Author

Robert Price, Mar 05 2016

Status

approved