2-CA Fractal Replicators

Mirek's MCell is perhaps the most comprehensive Windows application for playing with Cellular Automata.

The following rules in the "Weighted Life" architecture will all result in fractal replicators, with differently shaped layouts. Any starting configuration of active cells in these CAs will be replicated endlessly in a self-similar layout

The first 9 values of each rule specify the weights of the neighbors being considered. "HI0" specifies that there are no history states or intermediate states between a cell's active and inactive states. "RSx" and "RBy" signify that a cell survives if x neighbors are active, and that a cell is born (becomes active if previously inactive) if y neighbors are active, respectively.

Triangular

NW1,NN0,NE1,WW0,ME0,EE0,SW0,SS0,SE0,HI0,RS0,RS2,RB1
Perfect Sierpinski layout

NW1,NN1,NE1,WW0,ME0,EE0,SW0,SS0,SE0,HI0,RS0,RS2,RB1,RB3
Double nested triangular layout

NW0,NN1,NE0,WW0,ME0,EE1,SW0,SS0,SE0,HI0,RS0,RS2,RB1
Angled Sierpinski layout (grows along a 45 degree diagonal)

NW0,NN1,NE0,WW0,ME0,EE0,SW0,SS0,SE1,HI0,RS0,RS2,RB1
Sharply angled Sierpinski layout

Rectangular

NW1,NN1,NE1,WW1,ME0,EE1,SW0,SS0,SE0,HI0,RS1,RS3,RS5,RB1,RB3,RB5
2:1 rectangles with an empty horizontal bar in the lower part

NW1,NN1,NE1,WW1,ME0,EE1,SW1,SS1,SE1,HI0,RS1,RS3,RS5,RS7,RB1,RB3,RB5,RB7
Upside down version of the previous rule

Square

NW0,NN1,NE1,WW0,ME0,EE1,SW0,SS0,SE0,HI0,RS0,RS2,RB1,RB3
Also known as Rule s1357/b1357 in a Life CA. Grows equally in all directions

Sujai Kumar, March 2005