A269629 First difference of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 630", based on the 5-celled von Neumann neighborhood.

4, 4, 12, 8, 16, 20, 24, 36, 8, 28, 20, 32, 48, 16, 56, 12, 148, 28, 52, 4, 76, 20, 112, 24, 96, 104, 24, -36, 204, -8, 164, 32, 352, -180, 304, -52, 200, -24, 232, -64, 200, 36, 188, -32, 284, 172, -24, 260, 128, 204, 128, -108, 256, -24, 396, -68, 172, 256

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

Table of n, a(n) for n=0..57.

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 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=630; 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}]

Crossrefs

Cf. A269523.

Sequence in context: A169648 A273742 A169710 * A241496 A273412 A206488

Adjacent sequences: A269626 A269627 A269628 * A269630 A269631 A269632

Keyword

sign,easy

Author

Robert Price, Mar 01 2016

Status

approved