Rule 045
1  Matrix
for n=7


c=0  c=1

2  Number of different rows and columns
For different center values 0 and 1, and for different n=1,2,..,12.
(r0) 2 4 4 10 18 42 82 196 382 858 1782 3610
(c0) 2 3 2 5 7 10 13 20 25 37 48 69
(r1) 2 4 8 8 14 26 58 124 282 622 1378 2972
(r1) 1 2 3 3 5 8 10 15 20 29 37 54
Maximal of the numbers above (d_{n})
3  Time evolution diagram
Time goes upwards. The values of the initial configuration can be
changed by clicking on the bottom row. A grey cell means that its value
is not specified.
4  Local rule
A dot stands for an unspecified cell.
1 1 0 1 . 0 . . .
000 011 110 01. 0.. 1.0 .00 .10 ..0
0 0 0 1 . . . . .
001 100 111 0.0 10. 1.1 .01 .11 ..1
1 1 . . 0 . . . .
010 101 00. 0.1 11. 1.. .0. .1. ...
5  Sensitivity
The sensibility of a cell is computed as follows. For every row n
in the diagram, the upper center cell depends on the 2n+1 cells of
row n. Let w in {0,1}^{2n+1} be a bit string with a single
1, selecting a cell. We compute the proportion of bitstrings u in
{0,1}^{2n+1} such that f^{n}(u) =/= f^{n}(u and
w). If it is 0, we color the cell yellow, otherwise we choose a color
between red and black depending on the proportion, 1 beeing black.
6  Symetric rules
reflexive  101

conjugate  75

reflexive conjugate  89
