A269568 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

4, 4, 12, 4, 12, 20, 12, 20, 12, 20, 12, 36, 36, 52, 52, 52, -28, 44, 4, 4, 76, 4, 44, 92, 52, 44, 84, 108, -44, 252, -20, 276, -148, 100, 44, -4, 12, -36, 116, 116, 36, 12, 108, 20, 84, 124, 132, 292, -180, 212, -12, 132, 12, 300, 228, 52, 196, 148, 36, 276

Offset: 0

Author

Robert Price, Feb 29 2016

Keywords

• sign
• easy

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, 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. A269522.

Programs

Mathematica

rule=622; 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}]