B2ci3ai/S2-i3

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77topaz
Posts: 1467
Joined: January 12th, 2018, 9:19 pm

B2ci3ai/S2-i3

Post by 77topaz » February 23rd, 2018, 4:56 pm

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:

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x = 34, y = 19, rule = B2ci3ai/S2-i3
9bo10bo$8bobo8bobo$7bobobo6bo3bo$6bobo3bo4bobobobo$5bobo3bobo2bobo2bo2b2o$4bo
bo3bobo2bo3b2o5bo2bo$3bobo3bobo4bobo2bo3bob2obo$2bo3bobo2bo4bo2b2o5bo4bo$bo2b
2o3b2o4bob2o2bo2bo4bo2bo$o2bo2bobo7bo2b2ob2ob3o2bo2bo$bo2b2o3b2o4bob2o2bo2bo
4bo2bo$2bo3bobo2bo4bo2b2o5bo4bo$3bobo3bobo4bobo2bo3bob2obo$4bobo3bobo2bo3b2o
5bo2bo$5bobo3bobo2bobo2bo2b2o$6bobo3bo4bobobobo$7bobobo6bo3bo$8bobo8bobo$9bo
10bo!
However, there are also numerous non-trivial high-period rotors, such as these four (p21, p26, p30, p33):

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x = 63, y = 14, rule = B2ci3ai/S2-i3
21bo$20bobo13bo19bo$5bo2bo10bo3bo11bobo17bobo$4bob2obo8bo5bo11bo17bo3b
o$3bo4bo9bo5bo11bo16bo5bo$2bobobo10bo7bo9bo16bo5bobo$bo3bo10bo4bo4bo7b
o16bo7bobo$obobobo8bo4bobo4bo5bo5bobo8bobo6bo2bo$bobobo10bob2o3b2obo7b
o5bobo8bo6bo2bo$2bo3bo10bo2bobo2bo9bo4bo2bo8bo4bo2bo$3bobo12bo2bo2bo
10bo3bo2bo10bo3bobo$4bo14bo3bo12b2obobo12bo3bo$20bobo15bobo14bobo$21bo
17bo16bo!
There are also XOR-based one-dimensional rotors, such as this natural p62:

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x = 14, y = 15, rule = B2ci3ai/S2-i3
5bo$4bo$3bobo$2bo3bo$bo2bo2bo$o2bobo2bo$bo2bo4bo$2bo4bo2bo$3bob2obo2bo$4bo2bo
bo2bo$5bobobo3bo$6bobobobo$7bo3bo$8bobo$9bo!
There are several natural c/4 diagonal spaceships:

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x = 42, y = 9, rule = B2ci3ai/S2-i3
4bo31bo$b3obo29bobo$bo2bo11bobo15bo$o14bob3o13bobo$bobo12bo2bo14bobo$o
bo17bo14bo2bobo$bobo15bo15bo3bobo$2bo15bo16b2obobo$37bobo!
And finally, there is natural infinite growth in the form of several different wickstretchers:

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x = 54, y = 18, rule = B2ci3ai/S2-i3
40bo$38b2obo$37b2o3bo$6bo31bo$3bobobo29bobo$2b3obobo15bo13bo3bobo$2bo
2bo3bo11bobobo13bobobobo$bo18b3obobo13bobobobo$obo17bo2bo3bo13bo2bo2bo
$bobo15bo8bo13bo2b2obo$2bo17bo8bo13bo3bobo$3bobo15bo6bobo13bobo3bo$4bo
bo20bobobo13bobo3bo$5bobo20bo3bo13bob2o2bo$6bobo20bobobo13bo2bo2bo$7bo
bo20bo3bo13bobobo$8bobo20bobo15bobo$9bo22bo17bo!

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77topaz
Posts: 1467
Joined: January 12th, 2018, 9:19 pm

Re: B2ci3ai/S2-i3

Post by 77topaz » March 7th, 2018, 11:31 pm

A new unique high-period rotor, p24:

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x = 13, y = 12, rule = B2ci3ai/S2-i3
6bo$5bobo$4bobobo2bo$3bobo3b2obo$2bo5bo2bo$bo$obo$2o3$3b2o$3b2o!
And a new natural wickstretcher:

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x = 15, y = 15, rule = B2ci3ai/S2-i3
9bo$8bobo$7bobob3o$6bo3bo2bo$5bobo6bo$4bo6bobo$3bobo6bobo$2bo3bo4bobo$
bobobo6bo$o3bo4bobo$bobo4bobo$2bo4bobo$6bobo$5bobo$6bo!

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77topaz
Posts: 1467
Joined: January 12th, 2018, 9:19 pm

Re: B2ci3ai/S2-i3

Post by 77topaz » March 14th, 2018, 5:52 am

Another new type of natural wickstretcher:

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x = 13, y = 15, rule = B2ci3ai/S2-i3
4bo$3bobo$2bo3bo$bo2b2obo$o2bo2bobo$bobobo3bo$2bobo5bo$3bo7bo$10bobo$
6bo2bobo$5bo4bo$4bo2bo2b2o$5bobob2o$6bobo$7bo!

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