A269714 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood.

3, 4, 4, 8, 4, 20, -16, 24, 4, 48, -48, 48, 8, 100, -152, 56, 4, 112, -112, 112, 8, 224, -344, 112, 8, 224, -224, 224, 16, 452, -808, 120, 4, 240, -240, 240, 8, 480, -728, 240, 8, 480, -480, 480, 16, 960, -1704, 240, 8, 480, -480, 480, 16, 960, -1456, 480

Offset: 0

Author

Robert Price, Mar 04 2016

Keywords

• sign
• easy

Comments

Initialized with a single black (ON) cell at stage zero.

Rules 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692 and 700 also generate this sequence.

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

Crossrefs

Cf. A269711.

Programs

Mathematica

rule=20; 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 *)