Rule 045

1 - Matrix

for n=7
c=0c=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 (dn)

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 fn(u) =/= fn(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