A266672 - OEIS

A266672

Triangle read by rows giving successive states of cellular automaton generated by "Rule 57" initiated with a single ON (black) cell.

1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

COMMENTS

Row n has length 2n+1.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..10000

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 Elementary Cellular Automata

EXAMPLE

The first ten rows:

0 0 1

0 1 0 1 0

1 0 0 1 0 1 1

0 0 1 0 0 1 1 0 0

1 1 0 0 1 0 1 0 1 1 1

0 0 0 1 0 0 1 0 1 1 0 0 0

1 1 1 0 0 1 0 0 1 1 0 1 1 1 1

0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0

1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1

MATHEMATICA

rule=57; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

CROSSREFS

Sequence in context: A121559 A004641 A266441 * A266070 A262855 A353380

Adjacent sequences: A266669 A266670 A266671 * A266673 A266674 A266675

KEYWORD

nonn,tabf,easy

AUTHOR

Robert Price, Jan 02 2016

STATUS

approved

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