A269756 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 30", based on the 5-celled von Neumann neighborhood.

4, 7, 4, 20, -12, 36, -16, 72, -72, 84, -8, 80, -56, 116, -16, 52, -28, 100, 24, -4, -4, 108, 100, -28, -60, 252, 36, -36, -44, 180, 168, -224, 40, 276, 148, -76, -132, 220, 376, -292, -84, 472, 192, -300, -32, 340, 344, -240, -236, 524, 440, -472, -268, 756

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..299

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=30; 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. A269753.

Sequence in context: A101159 A339948 A270136 * A166530 A011518 A132265

Adjacent sequences: A269753 A269754 A269755 * A269757 A269758 A269759

Keyword

sign,easy

Author

Robert Price, Mar 04 2016

Status

approved