|
|
A273748
|
|
Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 918", based on the 5-celled von Neumann neighborhood.
|
|
1
|
|
|
1, 6, 15, 40, 69, 122, 175, 272, 373, 506, 663, 888, 1101, 1370, 1639, 2044, 2437, 2866, 3363, 3980, 4549, 5194, 5879, 6752, 7581, 8478, 9419, 10592, 11721, 12914, 14163, 15664, 17125, 18702, 20363, 22144, 23981, 26058, 28075, 30340, 32665, 35026, 37491
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
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
|
|
|
MATHEMATICA
|
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=918; stages=128;
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[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|