## B2ci3ai/S2-i3

For discussion of other cellular automata.

### B2ci3ai/S2-i3

This is a rule with a lot of interesting behaviour. Firstly, it supports spaceships and infinite growth, but it also shows some of the collapsing-down-to-diamond-shaped-patterns behaviour of rules which do not allow patterns to escape their bounding diamonds.

There is a large variety of oscillators (mainly billiard tables) with numerous different periods. Some of these periods are the result of several separate rotors being connected by the same stator, such as this impressive natural p168 object with four separate rotors:
`x = 34, y = 19, rule = B2ci3ai/S2-i39bo10bo\$8bobo8bobo\$7bobobo6bo3bo\$6bobo3bo4bobobobo\$5bobo3bobo2bobo2bo2b2o\$4bobo3bobo2bo3b2o5bo2bo\$3bobo3bobo4bobo2bo3bob2obo\$2bo3bobo2bo4bo2b2o5bo4bo\$bo2b2o3b2o4bob2o2bo2bo4bo2bo\$o2bo2bobo7bo2b2ob2ob3o2bo2bo\$bo2b2o3b2o4bob2o2bo2bo4bo2bo\$2bo3bobo2bo4bo2b2o5bo4bo\$3bobo3bobo4bobo2bo3bob2obo\$4bobo3bobo2bo3b2o5bo2bo\$5bobo3bobo2bobo2bo2b2o\$6bobo3bo4bobobobo\$7bobobo6bo3bo\$8bobo8bobo\$9bo10bo!`

However, there are also numerous non-trivial high-period rotors, such as these four (p21, p26, p30, p33):
`x = 63, y = 14, rule = B2ci3ai/S2-i321bo\$20bobo13bo19bo\$5bo2bo10bo3bo11bobo17bobo\$4bob2obo8bo5bo11bo17bo3bo\$3bo4bo9bo5bo11bo16bo5bo\$2bobobo10bo7bo9bo16bo5bobo\$bo3bo10bo4bo4bo7bo16bo7bobo\$obobobo8bo4bobo4bo5bo5bobo8bobo6bo2bo\$bobobo10bob2o3b2obo7bo5bobo8bo6bo2bo\$2bo3bo10bo2bobo2bo9bo4bo2bo8bo4bo2bo\$3bobo12bo2bo2bo10bo3bo2bo10bo3bobo\$4bo14bo3bo12b2obobo12bo3bo\$20bobo15bobo14bobo\$21bo17bo16bo!`

There are also XOR-based one-dimensional rotors, such as this natural p62:
`x = 14, y = 15, rule = B2ci3ai/S2-i35bo\$4bo\$3bobo\$2bo3bo\$bo2bo2bo\$o2bobo2bo\$bo2bo4bo\$2bo4bo2bo\$3bob2obo2bo\$4bo2bobo2bo\$5bobobo3bo\$6bobobobo\$7bo3bo\$8bobo\$9bo!`

There are several natural c/4 diagonal spaceships:
`x = 42, y = 9, rule = B2ci3ai/S2-i34bo31bo\$b3obo29bobo\$bo2bo11bobo15bo\$o14bob3o13bobo\$bobo12bo2bo14bobo\$obo17bo14bo2bobo\$bobo15bo15bo3bobo\$2bo15bo16b2obobo\$37bobo!`

And finally, there is natural infinite growth in the form of several different wickstretchers:
`x = 54, y = 18, rule = B2ci3ai/S2-i340bo\$38b2obo\$37b2o3bo\$6bo31bo\$3bobobo29bobo\$2b3obobo15bo13bo3bobo\$2bo2bo3bo11bobobo13bobobobo\$bo18b3obobo13bobobobo\$obo17bo2bo3bo13bo2bo2bo\$bobo15bo8bo13bo2b2obo\$2bo17bo8bo13bo3bobo\$3bobo15bo6bobo13bobo3bo\$4bobo20bobobo13bobo3bo\$5bobo20bo3bo13bob2o2bo\$6bobo20bobobo13bo2bo2bo\$7bobo20bo3bo13bobobo\$8bobo20bobo15bobo\$9bo22bo17bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: B2ci3ai/S2-i3

A new unique high-period rotor, p24:
`x = 13, y = 12, rule = B2ci3ai/S2-i36bo\$5bobo\$4bobobo2bo\$3bobo3b2obo\$2bo5bo2bo\$bo\$obo\$2o3\$3b2o\$3b2o!`

And a new natural wickstretcher:
`x = 15, y = 15, rule = B2ci3ai/S2-i39bo\$8bobo\$7bobob3o\$6bo3bo2bo\$5bobo6bo\$4bo6bobo\$3bobo6bobo\$2bo3bo4bobo\$bobobo6bo\$o3bo4bobo\$bobo4bobo\$2bo4bobo\$6bobo\$5bobo\$6bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: B2ci3ai/S2-i3

Another new type of natural wickstretcher:
`x = 13, y = 15, rule = B2ci3ai/S2-i34bo\$3bobo\$2bo3bo\$bo2b2obo\$o2bo2bobo\$bobobo3bo\$2bobo5bo\$3bo7bo\$10bobo\$6bo2bobo\$5bo4bo\$4bo2bo2b2o\$5bobob2o\$6bobo\$7bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm