Revision History for A278466
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
|
|
A278466
|
|
Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 49", based on the 5-celled von Neumann neighborhood.
(history;
published version)
|
|
|
#7 by Bruno Berselli at Wed Nov 23 02:51:21 EST 2016
|
|
|
|
#6 by Robert Price at Tue Nov 22 21:37:26 EST 2016
|
|
|
|
#5 by Robert Price at Tue Nov 22 21:37:21 EST 2016
|
|
|
|
#4 by Robert Price at Tue Nov 22 21:32:39 EST 2016
|
| LINKS
|
Robert Price, <a href="/A278466/a278466.tmp.txt">Diagrams of first 20 stages</a>
Robert Price, <a href="/A278466/a278466.tmp.txt">Diagrams of first 20 stages</a>
|
|
|
|
#3 by Robert Price at Tue Nov 22 21:32:23 EST 2016
|
| LINKS
|
Robert Price, <a href="/A278466/b278466.txt">Table of n, a(n) for n = 0..126</a>
Robert Price, <a href="/A278466/a278466.tmp.txt">Diagrams of first 20 stages</a>
|
|
|
|
#2 by Robert Price at Tue Nov 22 21:31:51 EST 2016
|
| NAME
|
allocatedBinary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 49", based on the 5-celled forvon RobertNeumann Priceneighborhood.
|
| DATA
|
1, 0, 1, 1100, 1, 111100, 1, 11111100, 1001, 1111100000, 1111, 111111100000, 1111, 11111111100100, 1, 1111111111111100, 11001001, 111111111000000000, 11111111, 11111111111001001100, 1, 1111111111111111111100, 1101011001, 111111111111100010000000, 1010111111
|
| OFFSET
|
0,4
|
| 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
|
N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
<a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
<a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
<a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
|
| MATHEMATICA
|
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=49; 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}];
Table[FromDigits[Part[ca[[i]][[i]], Range[1, i]], 10], {i, 1, stages-1}]
|
| KEYWORD
|
allocated
nonn,easy
|
| AUTHOR
|
Robert Price, Nov 22 2016
|
| STATUS
|
approved
editing
|
|
|
|
#1 by Robert Price at Tue Nov 22 21:31:51 EST 2016
|
| NAME
|
allocated for Robert Price
|
| KEYWORD
|
allocated
|
| STATUS
|
approved
|
|
|
|
|