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A269880
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 4", based on the 5-celled 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
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.
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+1-n, k-1+n]], {j, k+1-n, k-1+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
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 06 2016
STATUS
approved