

A269880


First differences of number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 4", based on the 5celled von Neumann neighborhood.


1



3, 0, 12, 12, 12, 0, 48, 60, 12, 0, 48, 48, 48, 0, 192, 252, 12, 0, 48, 48, 48, 0, 192, 240, 48, 0, 192, 192, 192, 0, 768, 1020, 12, 0, 48, 48, 48, 0, 192, 240, 48, 0, 192, 192, 192, 0, 768, 1008, 48, 0, 192, 192, 192, 0, 768, 960, 192, 0, 768
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OFFSET

0,1


COMMENTS

Initialized with a single black (ON) cell at stage zero.
First differences of A102376.


REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.


LINKS

Robert Price, Table of n, a(n) for n = 0..127
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 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


MATHEMATICA

code=4; stages=100;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1n, k1+n]], {j, k+1n, k1+n}], {n, 1, k}];
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 *)


CROSSREFS

Cf. A102376.
Sequence in context: A249010 A071534 A336667 * A135687 A057374 A269035
Adjacent sequences: A269877 A269878 A269879 * A269881 A269882 A269883


KEYWORD

sign,easy


AUTHOR

Robert Price, Mar 06 2016


STATUS

approved



