## Find a rule game

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.

### Find a rule game

I will post a challenge every week and you'll find/create a rule to compete. The rules that perform the best will be listed at the end of every week.

Week 1 Challenge:
Find a Life-like (Totalistic 2 state) rule which the following pattern stabilises within 100000 generations and has the maximum end population (if the population oscillates then the max population counts)
`x = 8, y = 7, rule = B3/S23\$2b4o\$5b2o\$2bob2o\$2b3o\$3bo!`

My record is 840 cells
Sarp

Posts: 191
Joined: March 1st, 2015, 1:28 pm

### Re: Find a rule game

Totalistic is too easy.

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Find a rule game

KittyTac wrote:Totalistic is too easy.

There are 131072 possible totalistic rules. I don't think anybody will search them all
Sarp

Posts: 191
Joined: March 1st, 2015, 1:28 pm

### Re: Find a rule game

I think I found the rule with 840:
`x = 5, y = 5, rule = B3678/S12456784o\$3b2o\$ob2o\$3o\$bo!`

I don't know if it can get higher through similar means.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 997
Joined: July 1st, 2016, 3:58 pm

### Re: Find a rule game

Sarp wrote:
KittyTac wrote:Totalistic is too easy.

There are 131072 possible totalistic rules. I don't think anybody will search them all

There are only a few totalistic rules that do not eternally explode or collapse immediately. There are about 100 interesting ones, I think.

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Find a rule game

KittyTac wrote:
Sarp wrote:
KittyTac wrote:Totalistic is too easy.

There are 131072 possible totalistic rules. I don't think anybody will search them all

There are only a few totalistic rules that do not eternally explode or collapse immediately. There are about 100 interesting ones, I think.

I agree that.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

Somewhat off-topic (or maybe it could be considered a new challenge?): with such a figure (~100 rules), we could actually attempt to create an exhaustive list of "interesting" totalistic Life-like CA.

77topaz

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

### Re: Find a rule game

Week 2 challenge
Find a Three state totalistic rule that has the highest amount of space ships that fit in a 10x10 bounding box in at least 1 generation
Sarp

Posts: 191
Joined: March 1st, 2015, 1:28 pm

### Re: Find a rule game

Sarp wrote:Week 2 challenge
Find a Three state totalistic rule that has the highest amount of space ships that fit in a 10x10 bounding box in at least 1 generation

THREE state means generations?
You need to use computers to check this
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

@Sarp, I'll try to find a solution of Week 2 challege in the "generations" rule set.
EDIT: Hopefully, I found this rule: /2/3.
Soup will usually creates a mess, but if you take a closer look on the chaotic growing mess, you'll find LOTS of spaceship travels at light-speed.
Spaceship families:
`x = 28, y = 10, rule = /2/34.2A20.2A\$4.2B19.A2B\$3.A20.AB\$3.B19.AB\$2.A19.AB\$2.B18.AB\$.A18.AB\$.B17.AB\$A17.AB\$B17.B!`

EDIT: First diag ship:
`x = 4, y = 4, rule = /2/32.A\$.BAB\$A\$.B!`

It's c/4.
EDIT: This is sparky:
`x = 10, y = 5, rule = /2/37.AB\$6.AB.A\$.AB2.AB2.B\$AB.AB.AB\$AB!`
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

Hunting wrote:@Sarp, I'll try to find a solution of Week 2 challege in the "generations" rule set.
EDIT: Hopefully, I found this rule: /2/3.
Soup will usually creates a mess, but if you take a closer look on the chaotic growing mess, you'll find LOTS of spaceship travels at light-speed.
Spaceship families:
`x = 28, y = 10, rule = /2/34.2A20.2A\$4.2B19.A2B\$3.A20.AB\$3.B19.AB\$2.A19.AB\$2.B18.AB\$.A18.AB\$.B17.AB\$A17.AB\$B17.B!`

EDIT: First diag ship:
`x = 4, y = 4, rule = /2/32.A\$.BAB\$A\$.B!`

It's c/4.
EDIT: This is sparky:
`x = 10, y = 5, rule = /2/37.AB\$6.AB.A\$.AB2.AB2.B\$AB.AB.AB\$AB!`

That's one of the best-known rules, actually. It's pretty watchable on a torus.

`x = 80, y = 64, rule = /2/313\$60.AB\$59.AB\$58.AB\$57.AB\$56.AB\$55.AB\$54.AB\$53.AB\$52.AB\$51.AB\$50.AB\$49.AB\$48.AB\$47.AB\$46.AB\$45.AB\$44.AB\$43.AB\$42.AB\$41.AB\$40.AB\$39.AB\$38.AB\$37.AB\$36.AB\$35.AB\$34.AB\$33.AB\$32.AB\$31.AB\$30.AB\$29.AB.A\$24.AB2.AB2.B\$23.AB.AB.AB\$23.AB!`

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Find a rule game

KittyTac wrote:
Hunting wrote:@Sarp, I'll try to find a solution of Week 2 challege in the "generations" rule set.
EDIT: Hopefully, I found this rule: /2/3.
Soup will usually creates a mess, but if you take a closer look on the chaotic growing mess, you'll find LOTS of spaceship travels at light-speed.
Spaceship families:
`x = 28, y = 10, rule = /2/34.2A20.2A\$4.2B19.A2B\$3.A20.AB\$3.B19.AB\$2.A19.AB\$2.B18.AB\$.A18.AB\$.B17.AB\$A17.AB\$B17.B!`

EDIT: First diag ship:
`x = 4, y = 4, rule = /2/32.A\$.BAB\$A\$.B!`

It's c/4.
EDIT: This is sparky:
`x = 10, y = 5, rule = /2/37.AB\$6.AB.A\$.AB2.AB2.B\$AB.AB.AB\$AB!`

That's one of the best-known rules, actually. It's pretty watchable on a torus.

`x = 80, y = 64, rule = /2/313\$60.AB\$59.AB\$58.AB\$57.AB\$56.AB\$55.AB\$54.AB\$53.AB\$52.AB\$51.AB\$50.AB\$49.AB\$48.AB\$47.AB\$46.AB\$45.AB\$44.AB\$43.AB\$42.AB\$41.AB\$40.AB\$39.AB\$38.AB\$37.AB\$36.AB\$35.AB\$34.AB\$33.AB\$32.AB\$31.AB\$30.AB\$29.AB.A\$24.AB2.AB2.B\$23.AB.AB.AB\$23.AB!`

I know it's known. It's in the Golly Files. Folder: Patterns/Generations/What-a-mess.rle
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

@Hunting: care to provide a figure for how many spaceships exist which fit inside 10x10 bbox?

I suspect the answer is quite large - probably in the thousands even just counting p1 photons, depending on the definition of spaceship.

A different generations rule - /23/3 - might even beat Brian's Brain, at least I'm fairly sure it will based on the increase in number of p1 photons because it allows the following kinds of spaceship families in addition to those in /2/3:
`x = 4, y = 49, rule = /23/32.BA\$2.BA\$.BA\$.BA3\$2.BA\$2.BA\$2.BA3\$2.BA\$2.BA\$2.BA\$.BA3\$2.BA\$2.BA\$2.BA\$.BA\$BA3\$2.BA\$2.BA\$2.BA\$.BA\$.BA3\$2.BA\$2.BA\$.BA\$.BA\$.BA3\$2.BA\$2.BA\$2.BA\$2.BA3\$2.BA\$2.BA\$2.BA\$2.BA\$.BA!`

and maybe (depending on the definition of spaceship)
`x = 5, y = 3, rule = /23/3BA.BA\$BA.BA\$2.BA!`

@Sarp: An interesting challenge, I'm not sure that one week is sufficient time to allow for responses though. Also, I think the rules for this challenge are a bit vague. Perhaps you could provide a few clarifications:

1. What patterns should be considered as unique spaceships for the purpose of this challenge? For example, I think the second pattern above should count but what about patterns where the parts are less well connected, e.g.
`x = 5, y = 4, rule = /2/3BA\$BA\$3.BA\$3.BA!`
where the cell at (2,2) is influenced by cells from both parts, but the actual evolution of the two parts is not distinct from the separate parts due to the rules of this particular CA.

2. What is the definition of totalistic for this challenge? From the first challenge you evidently mean outer-totalistic and not strictly totalistic, but which multi-state rules are allowed. Some options:
• Generations rules (outer-totalistic rules with one history state, such as /2/3).
• totalistic or outer-totalistic rules where the total is the sum of all cell states in the neighbourhood. (Generations rules not allowed)
• totalistic or outer-totalistic rules where the total number of cells of both states is counted and used to determine the resulting state. (Generations rules allowed, as well as many more complex rules.)
The latest version of the 5S Project contains over 47,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

Posts: 1109
Joined: August 9th, 2013, 12:45 am

### Re: Find a rule game

wildmyron wrote:@Hunting: care to provide a figure for how many spaceships exist which fit inside 10x10 bbox?

I suspect the answer is quite large - probably in the thousands even just counting p1 photons, depending on the definition of spaceship.

A different generations rule - /23/3 - might even beat Brian's Brain, at least I'm fairly sure it will based on the increase in number of p1 photons because it allows the following kinds of spaceship families in addition to those in /2/3:
`x = 4, y = 49, rule = /23/32.BA\$2.BA\$.BA\$.BA3\$2.BA\$2.BA\$2.BA3\$2.BA\$2.BA\$2.BA\$.BA3\$2.BA\$2.BA\$2.BA\$.BA\$BA3\$2.BA\$2.BA\$2.BA\$.BA\$.BA3\$2.BA\$2.BA\$.BA\$.BA\$.BA3\$2.BA\$2.BA\$2.BA\$2.BA3\$2.BA\$2.BA\$2.BA\$2.BA\$.BA!`

and maybe (depending on the definition of spaceship)
`x = 5, y = 3, rule = /23/3BA.BA\$BA.BA\$2.BA!`

@Sarp: An interesting challenge, I'm not sure that one week is sufficient time to allow for responses though. Also, I think the rules for this challenge are a bit vague. Perhaps you could provide a few clarifications:

1. What patterns should be considered as unique spaceships for the purpose of this challenge? For example, I think the second pattern above should count but what about patterns where the parts are less well connected, e.g.
`x = 5, y = 4, rule = /2/3BA\$BA\$3.BA\$3.BA!`
where the cell at (2,2) is influenced by cells from both parts, but the actual evolution of the two parts is not distinct from the separate parts due to the rules of this particular CA.

2. What is the definition of totalistic for this challenge? From the first challenge you evidently mean outer-totalistic and not strictly totalistic, but which multi-state rules are allowed. Some options:
• Generations rules (outer-totalistic rules with one history state, such as /2/3).
• totalistic or outer-totalistic rules where the total is the sum of all cell states in the neighbourhood. (Generations rules not allowed)
• totalistic or outer-totalistic rules where the total number of cells of both states is counted and used to determine the resulting state. (Generations rules allowed, as well as many more complex rules.)

wildmyron, 1. History cells doesnt count.
2. I guess the third definition is right.
P. S. you'll never beat me. Just go on and you'll see.(keep the rhyme!)
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

Hunting wrote:wildmyron, 1. History cells doesnt count.

What do you mean? In which tally do history cells not count (according to you)?

Hunting wrote:2. I guess the third definition is right.

The traditional definition is #2 in my list, which is why I asked for clarification.

Hunting wrote:P. S. you'll never beat me. Just go on and you'll see.(keep the rhyme!)

Oh no, give me mercy.
The latest version of the 5S Project contains over 47,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

Posts: 1109
Joined: August 9th, 2013, 12:45 am

### Re: Find a rule game

wildmyron wrote:
Hunting wrote:wildmyron, 1. History cells doesnt count.

What do you mean? In which tally do history cells not count (according to you)?

Hunting wrote:2. I guess the third definition is right.

The traditional definition is #2 in my list, which is why I asked for clarification.

Hunting wrote:P. S. you'll never beat me. Just go on and you'll see.(keep the rhyme!)

Oh no, give me mercy.

1. History cells cannot create births, so no interactions,then the spaceship is trivial, doesnt count.
2. ?
3. ...
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

This is kind of a joke, but
`@RULE 3StateYes, this is a "troll"@TABLEn_states:3neighborhood:oneDimensionalsymmetries:nonevar a = {0,1,2}var b={1,2}var c={1,2}0,b,a,bb,0,c,0b,0,0,0`

`x = 35, y = 24, rule = 3State7.A6.A.A\$5.3A7.3B\$4.A2.A7.3B\$16.2B10.A\$15.3A10.A\$26.2B3\$9.4A5.B13.B\$.A2.B4.4B6.2A10.3A\$2B.A5.2B.B5.4A9.2B\$.4A3.B.3A8.A\$2.3A5.2A8.2A\$4.A\$3.2B2\$8.3B.A19.3A\$8.5A19.2A\$8.2A.2A19.B\$8.B.2A8.2B\$10.2B8.B.2A\$11.B9.2A.2A\$22.3B\$21.B3.A!`
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

Posts: 2890
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Find a rule game

Saka wrote:This is kind of a joke, but
`@RULE 3StateYes, this is a "troll"@TABLEn_states:3neighborhood:oneDimensionalsymmetries:nonevar a = {0,1,2}var b={1,2}var c={1,2}0,b,a,bb,0,c,0b,0,0,0`

`x = 35, y = 24, rule = 3State7.A6.A.A\$5.3A7.3B\$4.A2.A7.3B\$16.2B10.A\$15.3A10.A\$26.2B3\$9.4A5.B13.B\$.A2.B4.4B6.2A10.3A\$2B.A5.2B.B5.4A9.2B\$.4A3.B.3A8.A\$2.3A5.2A8.2A\$4.A\$3.2B2\$8.3B.A19.3A\$8.5A19.2A\$8.2A.2A19.B\$8.B.2A8.2B\$10.2B8.B.2A\$11.B9.2A.2A\$22.3B\$21.B3.A!`

"nice" solution - almost everything is a spaceship.
BUT remember Sarp says "totalistic" - your symmetries is none, so it's non-isotropic non-totalistic.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

Week 3 Challenge: Find a 3-state rule with the the slowest 1-cell spaceship.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 726
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Find a rule game

gameoflifemaniac wrote:Week 3 Challenge: Find a 3-state rule with the the slowest 1-cell spaceship.

Difficulty level: Golly Hard.
At first, symmetric rules can not do that. So we need some rule like this:
`x=1,y=1,rule=MAPAASAAA/3o!`

This is not a valid solution(or an almost solution, because the history cell doesn't matter, I think).
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

Hunting wrote:
gameoflifemaniac wrote:Week 3 Challenge: Find a 3-state rule with the the slowest 1-cell spaceship.

Difficulty level: Golly Hard.
At first, symmetric rules can not do that. So we need some rule like this:
`x=1,y=1,rule=MAPAASAAA/3o!`

This is not a valid solution(or an almost solution, because the history cell doesn't matter, I think).

I meant any of the 2^19683 3-state rules.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 726
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Find a rule game

This thread tried to find the answer for n-states. The record for 3 states was C/36 by toroidalet.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 997
Joined: July 1st, 2016, 3:58 pm

### Re: Find a rule game

Week 4 Challenge
Find a 2 state rule and a shape fitting in a 10x10 bounding box so that the shape stabilises in as many generations as possible (A shape stabilizes when it becomes only still lifes, oscillators, spaceships, linear growths and/or replicators that won't interact with eachother). if the shape doesn't stabilise it doesn't qualify.
Sarp

Posts: 191
Joined: March 1st, 2015, 1:28 pm

### Re: Find a rule game

Sarp wrote:Week 4 Challenge
Find a 2 state rule and a shape fitting in a 10x10 bounding box so that the shape stabilises in as many generations as possible (A shape stabilizes when it becomes only still lifes, oscillators, spaceships, linear growths and/or replicators that won't interact with eachother). if the shape doesn't stabilise it doesn't qualify.

Hard! Very very very very HARD!
I'll post:
B3/S23, and this:
`x = 6, y = 4, rule = B3/S23ob3o\$o4bo\$obobo\$bo2bo!`

Hmmmm, It's 17465 gen.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1025
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Find a rule game

Hunting wrote:
Sarp wrote:Week 4 Challenge
Find a 2 state rule and a shape fitting in a 10x10 bounding box so that the shape stabilises in as many generations as possible (A shape stabilizes when it becomes only still lifes, oscillators, spaceships, linear growths and/or replicators that won't interact with eachother). if the shape doesn't stabilise it doesn't qualify.

Hard! Very very very very HARD!
I'll post:
B3/S23, and this:
`x = 6, y = 4, rule = B3/S23ob3o\$o4bo\$obobo\$bo2bo!`

Hmmmm, It's 17465 gen.

There's Simon Ekström's 9-by-6 version of Lidka:
`x = 9, y = 6, rule = B3/S236bo\$6b3o2\$3b2o3bo\$3bo4bo\$3o5bo!`
(29126 generations)

Macbi

Posts: 659
Joined: March 29th, 2009, 4:58 am

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