A202857 Value of the one-dimensional radius 2 totalistic 2-color cellular automaton rule 20 after 1 step, with initial condition n.

0, 0, 15, 0, 7, 15, 17, 0, 3, 7, 19, 15, 25, 17, 45, 0, 1, 3, 23, 7, 27, 19, 41, 15, 29, 25, 107, 17, 37, 45, 85, 0, 0, 1, 31, 3, 31, 23, 33, 7, 31, 27, 99, 19, 33, 41, 93, 15, 31, 29, 231, 25, 99, 107, 217, 17, 33, 37, 155, 45, 93, 85, 165, 0, 0, 0, 15, 1

Offset

1,3

Comments

The initial pattern is the binary representation of n. A cell becomes live in the next step if either 2 or 4 of its neighbors (including itself) was live in the previous step. The output is interpreted as a binary integer, with factors of 2 removed.

Links

Table of n, a(n) for n=1..68.

Eric W. Weisstein, Totalistic Cellular Automaton.

Stephen Wolfram, A New Kind of Science, page 281.

Index entries for sequences related to cellular automata

Formula

a(2n) = a(n).

Example

For n=3, the system's evolution for 1 step is:
  001100 = 3,
  011110 = 15.

Mathematica

input[x_] := RealDigits[x, 2]; step[x_] := Flatten[CellularAutomaton[{20, {2, 1}, 2}, {Part[input[x], 1], 0}, {{1}}]]; a[x_] := FromDigits[step[x], 2]; Table[a[n], {n, 100}]

Crossrefs

Sequence in context: A271763 A362267 A271339 * A055965 A067154 A187486

Adjacent sequences: A202854 A202855 A202856 * A202858 A202859 A202860

Keyword

nonn

Author

Ben Branman, Dec 25 2011

Status

approved