## Gems (B3457/S4568)

For discussion of other cellular automata.

### Gems (B3457/S4568)

The rule contains the famous c/5648 spaceship, currently the slowest known non-adjustable-speed spaceship in any range-1 Life-like rule.

`x = 12, y = 14, rule = B3457/S45684bo2bo\$4b4o\$2b8o\$2b2ob2ob2o\$obobo2bobobo\$2ob6ob2o\$ob3o2b3obo\$3ob4ob3o\$2ob6ob2o\$b3o4b3o\$b3o4b3o\$3b2o2b2o\$3bo4bo\$5b2o!`

This rule also supports high-period oscillators, such as this p62:
`x = 10, y = 10, rule = B3457/S45684bo\$2bobobo\$2b7o\$b7o\$2b8o\$8o\$2b7o\$b7o\$3bobobo\$5bo!`

p52:
`x = 8, y = 8, rule = B3457/S45683bobo\$bob3o\$2b3ob2o\$4ob2o\$2bob4o\$2ob3o\$2bobobo\$2bobo!`

p64:
`x = 9, y = 10, rule = B3457/S45684bo\$4b3o\$2b5o\$2bob5o\$5o2bo\$bo2b5o\$5obo\$2b5o\$2b3o\$4bo!`

p30:
`x = 8, y = 8, rule = B3457/S45684bo\$2b3obo\$2b4o\$ob6o\$b6o\$7o\$2b2o\$2bobo!`

I don't even know what period this one is:
`x = 9, y = 11, rule = B3457/S45685bo\$3bo\$3b5o\$b4o2bo\$bo2b2o2bo\$ob2o3bo\$bo2b2o2bo\$b4o2bo\$3b5o\$3bo\$5bo!`

This rule has dynamics similar to LongLife if searched on one-cell-thick soups, although I highly doubt this will result in any interesting patterns showing up:
http://catagolue.appspot.com/census/b3457s4568/1x256

Unfortunately this rule is explosive and cannot be conventionally soup searched.

Research has been conducted into seeing if any lower-period spaceships exist in this rule. Could any higher-period spaceships exist?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Gems (B3457/S4568)

muzik wrote:I don't even know what period this one is:
`x = 9, y = 11, rule = B3457/S45685bo\$3bo\$3b5o\$b4o2bo\$bo2b2o2bo\$ob2o3bo\$bo2b2o2bo\$b4o2bo\$3b5o\$3bo\$5bo!`

Talked to my good friend oscar.lua and he told me pretty much right away it was p706:
`x = 9, y = 11, rule = B3457/S45685bo\$3bo\$3b5o\$b4o2bo\$bo2b2o2bo\$ob2o3bo\$bo2b2o2bo\$b4o2bo\$3b5o\$3bo\$5bo![[ STOP 706 ]]`
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### Re: Gems (B3457/S4568)

An oscillator which closely resembles the spaceship:

`x = 15, y = 32, rule = B3457/S45685bobo\$5b2ob2o\$3b2obob2o\$3b2obo3b2o\$b5o5bo\$bob6obo2bo\$bob6obo2bo\$b5o5bo\$3b2obo3b2o\$3b2obob2o\$5b2ob2o\$5bobo5\$8bo\$6b3o\$6b2ob2o\$4b2o4bo\$4b2o3b4o\$2b2o2bo3bobo\$2b4o7b2o\$7o3b5o\$7o3b5o\$2b4o7b2o\$2b2o2bo3bobo\$4b2o3b4o\$4b2o4bo\$6b2ob2o\$6b3o\$8bo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Gems (B3457/S4568)

p258 and p434:
`x = 25, y = 61, rule = B3457/S45682\$10b4o\$10b4o\$8b8o\$8b8o\$6b12o\$7b2ob4ob2o\$7b2ob4ob2o\$9b6o\$9b6o2\$11b2o33\$10b4o\$10bo2bo\$8b8o\$8bo2b2o2bo\$6b2o3b2o3b2o\$7b10o\$7b3o4b3o\$9b6o\$9b6o2\$11b2o!`

p72:
`x = 7, y = 7, rule = B3457/S45682bobo\$2b3o\$o4b2o\$bo2b2o\$3ob2o\$2b2o\$2b2o!`

p98:
`x = 9, y = 9, rule = B3457/S45683bobo\$b2ob2o\$3b5o\$8o\$bo3b4o\$8o\$3b5o\$b2ob2o\$3bobo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Gems (B3457/S4568)

Possibly the happiest p26 I have ever seen:
`x = 20, y = 9, rule = B3457/S45683b2o10b2o\$15b2o\$b6o6b6o\$b6o6b6o\$ob4obo4bo2b2o2bo\$b6o6b6o\$2ob2ob2o4b2ob2ob2o\$2bo2bo8bo2bo\$2b4o8b4o!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland