ConwayLife.com

Posted: **March 22nd, 2016, 8:05 pm**

Saka wrote: B0 doesn't really mean birth on 0 neighbors ._.

I noticed, but can it still simulate >c ships on quicklife?

Posted: **March 22nd, 2016, 8:21 pm**

muzik wrote:
Saka wrote: B0 doesn't really mean birth on 0 neighbors ._.
I noticed, but can it still simulate >c ships on quicklife?

I extremely doubt it, but I think no

Posted: **March 22nd, 2016, 8:36 pm**

Kden. Are there any ways to have >c ships in rules with .rule format?

Posted: **March 22nd, 2016, 8:59 pm**

Saka wrote:
muzik wrote:Can someone make a rule in which spaceships travelling faster than light speed exist?
I'm pretty sure that's not possible in the current moore neighbor hood, but you can make FTL expanding cubes by putting
Code: Select all
0,0,0,0,0,0,0,0,0,1
into your rule file

Golly doesn't handle 0,0,0,0,0,0,0,0,0,1 properly (i.e. B0 in RuleLoader), so I wouldn't take "FTL expanding cubes" (which appear to expand exponentially by the way) as some kind of valid cellular automaton-related construct.

Posted: **March 27th, 2016, 6:57 pm**

M. I. Wright, 10 days ago, wrote:I'll take a crack at it in a few days

Here it is, albeit with a pretty liberal definition of 'few':

Code: Select all

@RULE 123456-3_234-23_a
@TABLE

n_states:3
neighborhood:Moore
symmetries:permute

var a={0,1}
var aa=a
var ab=a
var ac=a
var b={0,2}
var ba=b
var z={0,1,2}
var za=z
var zb=z
var zc=z
var zd=z
var ze=z
var zf=z
var zg=z

#state 1: B3
0,1,1,1,0,0,0,0,0,1

#state 1: D078
1,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1,1,0
1,0,0,0,0,0,0,0,0,0

#state 1: Death if state 2 > state 0 ior state 1 [I didn't remember how to properly use variables until after I finished this part, so it could obviously be optimized]
1,2,0,0,0,0,0,0,0,0
1,2,2,0,0,0,0,0,0,0
1,2,2,1,0,0,0,0,0,0
1,2,2,2,0,0,0,0,0,0
1,2,2,2,1,0,0,0,0,0
1,2,2,2,1,1,0,0,0,0
1,2,2,2,2,0,0,0,0,0
1,2,2,2,2,1,0,0,0,0
1,2,2,2,2,1,1,0,0,0
1,2,2,2,2,1,1,1,0,0
1,2,2,2,2,1,1,1,1,0
1,2,2,2,2,2,0,0,0,0
1,2,2,2,2,2,1,0,0,0
1,2,2,2,2,2,1,1,0,0
1,2,2,2,2,2,1,1,1,0
1,2,2,2,2,2,2,0,0,0
1,2,2,2,2,2,2,1,0,0
1,2,2,2,2,2,2,1,1,0
1,2,2,2,2,2,2,2,0,0
1,2,2,2,2,2,2,2,1,0
1,2,2,2,2,2,2,2,2,0

#state 2: B23
0,2,2,1,1,a,aa,ab,ac,2
0,2,2,2,1,1,a,aa,ab,2

#state 2: S234 + at least 1 of s1 [would probably be written like S234(s1>0) or something, but I don't really feel like inventing a whole new notation system]
2,2,2,b,ba,1,z,za,zb,2

#state 2: D015678
2,z,za,zb,zc,zd,ze,zf,zg,0

Admittedly not a very interesting rule. I ended up scrapping the fourth state to reduce complexity, meaning that the two states can't overlap, and I think that negatively impacted the relationship between them. To compensate for it, though, I also made this version of the rule which removes the restriction that a state 1 cell must die before being taken over by a state 2 cell (which actually kinda makes more sense in the context of 'prey vs. predator')

Code: Select all

@RULE 123456-3_234-23_b
@TABLE

n_states:3
neighborhood:Moore
symmetries:permute

var a={0,1}
var aa=a
var ab=a
var ac=a
var ad=a
var b={0,2}
var ba=b
var z={0,1,2}
var za=z
var zb=z
var zc=z
var zd=z
var ze=z
var zf=z
var zg=z

#state 1: B3
0,1,1,1,0,0,0,0,0,1

#state 1: D078
1,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1,1,0
1,0,0,0,0,0,0,0,0,0

#state 1: D(s2>s01) [I didn't remember how to properly use variables until after I finished this part, so it could obviously be optimized]
1,2,0,0,0,0,0,0,0,2
1,2,2,0,0,0,0,0,0,2
1,2,2,1,0,0,0,0,0,2
1,2,2,2,0,0,0,0,0,2
1,2,2,2,1,0,0,0,0,2
1,2,2,2,1,1,0,0,0,2
1,2,2,2,2,0,0,0,0,2
1,2,2,2,2,1,0,0,0,2
1,2,2,2,2,1,1,0,0,2
1,2,2,2,2,1,1,1,0,2
1,2,2,2,2,1,1,1,1,2
1,2,2,2,2,2,0,0,0,2
1,2,2,2,2,2,1,0,0,2
1,2,2,2,2,2,1,1,0,2
1,2,2,2,2,2,1,1,1,2
1,2,2,2,2,2,2,0,0,2
1,2,2,2,2,2,2,1,0,2
1,2,2,2,2,2,2,1,1,2
1,2,2,2,2,2,2,2,0,2
1,2,2,2,2,2,2,2,1,2
1,2,2,2,2,2,2,2,2,2

#state 2: B23
0,2,2,1,1,a,aa,ab,ac,2
0,2,2,2,1,1,a,aa,ab,2

#state 2: S234 + at least 1 of s1 [would probably be written like S234(s1>0) or something, but I don't really feel like inventing a whole new notation system]
2,2,2,b,ba,1,z,za,zb,2

#state 2: D015678
2,z,za,zb,zc,zd,ze,zf,zg,0

Far more interesting in the long run, as the predator state is now constantly 'eating' the prey state. For comparison, run the following soup in both rules:

Code: Select all

x = 10, y = 10, rule = 123456-3_234-23_a
B2ABA2.B.B$.A.B.B$A.B.2B.A.A$2A.AB.B2.A$A3.A3.2A$2.2A2.A$3AB.B2.BA$B.
A.B.B.B$B4.B.3B$3B2A.2BA!

...and to spare you the trouble, here's what it looks like after 100 generations in each rule:

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x = 54, y = 66, rule = 123456-3_234-23_a
20.3A.A$20.7A$18.3A2.A.2A5.A.A3.3A$16.3A.4A.3A2.7A.4A$16.A.A.A.A.2A.A
2.A2.A.A.2A.2A$15.2A.5A.A.9A.A.A.A.A$16.A.A2.A.3A.A.A.A2.12A$15.7A.A.
9A.A.A.A.2A.3A$17.A.A.A.A.A2.A.A.A.6A2.5A$15.3A.A.A.12A5.3A.3A$15.A.A
.4A.A.A2.A.A2.7A3.A$6.A.A.2A.6A.A.A.6A.3A2.A.A.5A$4.10A.A3.4A.A2.A.A.
A.2A.A.3A.A$2.3A.2A.A.A.7A2.A.8A2.A.A.A.3A$2.A.3A2.4A.A.A2.7A4.A.5A.
4A$.2A.A.3A.A.8A.A.A.6A.A.A.3A.2A$2.3A.A.5A.2A.A.6A.A.A.A.3A3.3A$3A.
3A.A3.3A2.3A.A3.6A.A.3A.A$3A.A.6A2.3A2.7A.A2.6A.3A$3A.3A4.3A2.3A.A.A
2.6A.A2.A.A.A$2.3A.6A2.3A.A.6A.A2.A.9A$.2A.3A2.A.4A.3A.A4.6A.A2.A2.A.
A$2.3A2.3A.A.A.2A.A.6A.A2.13A$.2A2.3A.3A.2A.3A.A.A2.6A.A.A.A2.A.A.A.A
$2.2A.A.3A.3A.2A.8A2.A.10A.7A$2.6A.3A.3A.A.A.A.A.5A.A.A.A3.2A2.A3.A$
4.A.4A.A3.A.3A.A.A.A.A.5A.4A.6A.2A$7.A3.7A.A.A.3A.A.A3.3AB.A.A4.3A.A$
13.A.A.3A.3A.5A.3A.3B8A.3A$15.3A.3A.3A3.3A.3AB.A6.3A.2A$16.2A.A.3A.A.
3A.2A.A.10A.3A$16.6A.5A.A.A.2A.2A2.A4.3A.2A$17.A.A.3A4.2A.3A.A.9A.3A$
18.4A.8A2.A.A.A2.2A.A3.A.2A$19.A.3A4.A.10A.10A$18.2A.A.8A.A.A.A2.A.A.
A.A.A2.3A$19.A.3A.A.A.A.11A.A.8A$18.4A.3A.3A.A.A.A.A.A.4A.A.2A.A$18.A
.A.2A.3A.A.A.8A.A.A.3A.2A$15.7A.3A2.4A.A4.A2.6A.3A$13.2A.2A.A.3A.2A.A
2.11A2.A.A.A.2A$12.5A2.3A.2A.6A4.A.A2.8A.A.A$12.2A2.3A2.4A.A.A2.11A.A
.2A.A.3A$13.4A.3A3.A.A.4A.A.A.A2.A.4A.3A2.2A$12.3A.3A.9A2.2A.7A.A2.A.
A.A.2A$12.2A.2A.4A.A.A2.7A3.A.8A.4A$13.2A.2A.A.8A2.A.A.4A.A2.A.A.4A$
12.10A.A4.4A.2A3.7A4.2A$11.A.2A2.A3.8A2.2A.5A.A.A$11.2A.4A.3A2.A.A2.
4A.A.A.A.3A$10.3A.A2.3A2.9A.A.A.A.A.A$11.7A.2A.A2.A.A2.A.11A$10.2A.A.
A.2A.13A2.A.A.A.A$11.A.3A.2A.A.A.A.A.A.A.3A.2A.4A$11.3A.3A.17A.A.A2.A
$11.A.3A.A.A.A2.A2.A.A.A.A.9A$12.2A2.4A.15A2.A2.3A$11.A.4A.A2.A.2A.A.
A.A.A2.7A$11.3A.A.7A3.4A.4A2.A.2A$10.2A2.4A.A.2A6.2A.A.A.5A$11.2A.A.
2A.3A7.8A3.2A$11.5A.A.2A10.A.A2.5A$13.A2.5A11.5A.A.3A$18.A13.4A.3A.2A
$34.A4.4A$39.3A!

(the predator pretty much became dormant, with only 5 of its cells staying alive. It doesn't affect the prey at all past generation 20 or so)

Code: Select all

x = 31, y = 28, rule = 123456-3_234-23_b
4.3A$3.4A$3.6A$3.A.A2.A$2.5A.2A$3.A2.A.A$2.2A.5A$3.A.A2.A$2.5A.2A$3.A
2BA.A$2.A4B3A$2.5B.A2$13.2A6.A$12.2BA4.5A$13.B3A.A.A.2A$13.B.6A2.2A$
3B11.3BA.A.3A$B2A13.3B3A.2A$A.2A13.2BA.A.A.A$3A14.2B7A.A$.A15.2BA.A.A
.5A$18.2B2A.3A3.A$19.2B2A2.3A.2A$20.2B3A2.3A$21.BA.A.2A$21.B6A$22.2A.
A!

(the predator state has a way more dynamic relationship with its prey, having remained active throughout the simulation)

The concept was a bit difficult to transcribe into a ruletable, so if I got something wrong let me know. I'd also love to experiment with this concept in other rules - something like Seeds/Morley would be pretty interesting.
note how I left the background color alone

Here's a great demonstration of the predator/prey relationship in the latter rule: a wick eater (state 2) destroys a wickstretcher (state 1):

Code: Select all

x = 8, y = 30, rule = 123456-3_234-23_b
3B2.3B$8B$3A3B2A$.A.A2BA$2A.5A$.A2.A.A$5A.2A$.A.A2.A$2A.5A$.A2.A.A$5A
.2A$.A.A2.A$2A.5A$.A2.A.A$5A.2A$.A.A2.A$2A.5A$.A2.A.A$5A.2A$.A.A2.A$
2A.5A$.A2.A.A$5A.2A$.A.A2.A$2A.5A$.A2.A.A$.4A.2A$3.A2.A$2.5A$3.2A!

I also found this extensible p2 oscillator (with both even and odd parity) - doesn't really show the predator/prey thing, but I thought it was neat:

Code: Select all

x = 10, y = 19, rule = 123456-3_234-23_b
2.A5.A$3AB2.3AB$.A2B3.A2B$.AB3.2AB$2A5.AB$.AB3.2A$.A5.AB$2AB4.A$.A4.
2AB$.AB4.A$2A5.AB$.AB3.2A$.A5.AB$2AB4.A$.AB3.2AB$.A2B3.AB$3AB3.A2B$2.
A3.3AB$8.A!

Edit: most of the billiard table oscillators that occur are period-2. I just found this p4, though:

Code: Select all

x = 7, y = 7, rule = 123456-3_234-23_b
A2.A2.A$7A$.A.B.A$AB3.BA$.A.B.A$7A$A2.A2.A!

Lastly: a glider!

Code: Select all

x = 5, y = 5, rule = 123456-3_234-23_b
.2B$2B2A$2B3A$2B2A$.2B!

Posted: **March 27th, 2016, 7:55 pm**

Minimal "seed ecosystem"?

Code: Select all

x = 3, y = 3, rule = 123456-3_234-23_b
2BA$BA$3A!

Posted: **March 27th, 2016, 9:18 pm**

Not-quite-a-spaceship:

Code: Select all

x = 18, y = 30, rule = 123456-3_234-23_b
5$3.2B3.2B$3.7BA$4.A.3BA$3.5A.2A$4.A.A2.A$3.2A.5A$4.A2.A.A$3.5A.2A$4.
A.A2.A$3.2A.5A$4.A2.A.A$3.5A.2A$4.A.A2.A$3.2A.5A$4.A2.A.A$4.6A$6.3A$
7.A!

Front=2c/6
Back=2c/4 Both glide symmetric
Edit: Another one

Code: Select all

x = 25, y = 23, rule = 123456-3_234-23_b
4.4A.5A$3.2A2.A.A2.A$4.7A.2A$3.2A2.A2.A.A$4.4A.5A$3.2A2.A.A2.A$4.6A2B
2A$3.2A.BA.3BA$4.2A3B2.3B$3.2A2B5.B$4.AB$3.2AB$4.A$3.2A$4.2A$3.2A$4.
2A$3.2A$4.2A$3.2A$4.2A$3.2A$4.2A!

And more

Code: Select all

x = 22, y = 5, rule = 123456-3_234-23_b
2.2A2.4A2.4A$3.4A2.4A2.2A$2.2A2.4A2.4A$2.9B2A2.2A$3.4B2.2B.4A!

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x = 16, y = 11, rule = 123456-3_234-23_b
8.2A2.4A$9.4A2.A$8.2A2.4A$9.4A2.A$8.2A2.4A$8.3B2A2.A$9.2B.4A$12.A2.A$
12.4A$11.2A2.A$12.4A!

Code: Select all

x = 40, y = 23, rule = 123456-3_234-23_b
2$10.BA.A.A.A.A.A.A.A.A.A.A.A.A.A.A$10.B29A$10.B.A.A.A.A.A.A.A.A.A.A.
A.A.A.A$11.BA.A.A.A.A.A.A.A.A.A.A.A.A.A$11.2B27A$11.2B.A3.A3.A3.A3.A
3.A3.A$12.2B3A.3A.3A.3A.3A.3A.2A$11.2B2A.3A.3A.3A.3A.3A.3A$11.BA3.A3.
A3.A3.A3.A3.A$12.28A$9.3BA.A.A.A.A.A.A.A.A.A.A.A.A.A$8.B.A.A.A.A.A.A.
A.A.A.A.A.A.A.A.A$8.B31A$8.BA.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A$8.2B.A.A.
A.A.A.A.A.A.A.A.A.A.A.A.A$8.2B30A$9.BA.A.A.A.A.A.A.A.A.A.A.A.A.A.A!

Code: Select all

x = 27, y = 18, rule = 123456-3_234-23_b
6.7A.4A$5.2A2.A2.A.A2.2A$6.4A.7A$5.2A2.A.A2.A2.2A$6.7A.4A$5.2A2.A.BA.
A2.2A$6.3A5B4A$5.2A4B.3B2.2A$6.A2B7.BA$5.2A2B7.B2A$6.AB8.BA$5.2A10.2A
$6.2A8.2A$5.2A10.2A$6.2A8.2A$5.2A10.2A$6.2A8.2A$5.2A10.2A!

Code: Select all

x = 28, y = 10, rule = 123456-3_234-23_b
19.2A$19.A$18.B2A$17.2BA$16.2B3A$8.4B.B.2BA.A$7.A4B6A.2A$8.4A2.A.A2.A
$7.2A2.4A.5A$8.4A2.A2.A.A!

Code: Select all

x = 31, y = 30, rule = 123456-3_234-23_b
6.2A$5.2A$6.2A$5.2A$6.2A$5.2A$6.2A$5.2A$6.A$5.2AB$6.A2B$5.3A2B$6.A.A
2B.B.2B$5.2A.6A4B$6.A2.A.A2.2A3B$5.5A.4A2.2A$6.A.A2.A2.4A$5.2A.7A2.2A
$6.A2.A.A2.4A$5.5A.4A2.2A$6.A.A2.A2.4A$5.2A.7A2.2A$6.A2.A.A2.4A$5.5A.
4A2.2A$6.A.A2.A2.4A$5.2A.7A2.2A$6.A2.A.A2.4A$5.5A.4A2.2A$6.A.A2.A2.4A
$5.2A.7A2.2A!

Wow. That's a lot.

Posted: **March 29th, 2016, 12:02 am**

The first one there was the fourth RLE in my original post.

BlinkerSpawn wrote:Minimal "seed ecosystem"?

Probably, I found another with 8 cells but it was 5x4. There might be one with 7 cells, but I'm pretty sure that the 3x3 bounding box is minimal.

Posted: **March 29th, 2016, 2:42 pm**

Very neat.

The overall effect seems to (largely) be that the prey population gets "chased" by the predators. One thing I expected to see but haven't stumbled on yet is something close to the classic predator-prey sine waves where population peaks and then declines with a phase shift of pi/4 or so. But maybe that'd require something the represents a time-lag.

Still, very neat patterns arising.

I'm curious about using Golly as a basis for modeling and studying systems generally.

For now, I'll keep looking at/for patterns in these rules.

Posted: **March 29th, 2016, 5:17 pm**

eze266 wrote:Very neat.

The overall effect seems to (largely) be that the prey population gets "chased" by the predators. One thing I expected to see but haven't stumbled on yet is something close to the classic predator-prey sine waves where population peaks and then declines with a phase shift of pi/4 or so. But maybe that'd require something the represents a time-lag.

Still, very neat patterns arising.

I'm curious about using Golly as a basis for modeling and studying systems generally.

For now, I'll keep looking at/for patterns in these rules.

This would likely require the predator-prey-superposition state that people are shying away from for the time being.

Posted: **March 31st, 2016, 9:05 am**

Some big c/6 spaceships:

Code: Select all

x = 46, y = 65, rule = 123456-3_234-23_b
6$8.A.A.A.A.A.A.A.A.A2B$6.20AB$6.A3.A3.A3.A2B2.A.AB$5.2A.3A.3A.2A2B$
5.4A.3A.3A2B$6.A.A3.A2.3B$8.7A2B$10.A.A.A.B$14.A2B$11.A.A.AB$9.7A$8.
2A.A3.AB$7.5A.3A2B$8.2A.3A.2A2B$9.A3.A3.A2B2.A.A2B$9.17AB$11.A.A.A.A.
A.A.A.AB7$20.A.A.A.A.A2B$18.11A2B$18.A3.A3.A4B$17.2A.3A.2A2B$18.3A.3A
2B$20.A3.AB$20.5AB$22.A.A$23.A2B$19.A.A.A.B$17.8A2B$17.A3.A3.2B$16.2A
.3A.3A2B$15.5A.3A.2A2B$16.2A.A3.A3.A2B2.A.AB$17.17A2B$19.A.A.A.A.A.A.
A.A2B$19.A.A.A.A.A.A.A.A2B$17.17A2B$16.2A.A3.A3.A2B2.A.AB$15.5A.3A.2A
2B$16.2A.3A.3A2B$17.A3.A3.2B$17.8A2B$19.A.A.A.B$23.A2B$22.A.A$20.5AB$
20.A3.AB$18.3A.3A2B$17.2A.3A.2A2B$18.A3.A3.A4B$18.11A2B$20.A.A.A.A.A
2B!

Posted: **April 9th, 2016, 7:51 pm**

I'd like a rule with two seperate types of cell that both act as B3/S23. They interact pretty normally, and count towards each other's birth counts (the one with the most neighbours of one colour wins that colour), but they do not count towards each others's death counts.

Hopefully you understood that, and can make it.

Posted: **April 20th, 2016, 6:35 pm**

Challenge: A rule where oscillators can have any odd period but no even period, with as few states as possible.

Posted: **April 29th, 2016, 6:28 am**

A rule where all three of these are c/4 diagonal ships?

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x = 10, y = 4, rule = tlife
obo3b2o$2o4b2o$bo4b2obo$8bo!

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x = 9, y = 3, rule = GlideLife
obo3bo$2o4bo$bo4b3o!

Posted: **April 29th, 2016, 7:11 pm**

A for awesome wrote:Challenge: A rule where oscillators can have any odd period but no even period, with as few states as possible.

Four states, including vacuum:

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@RULE Oddball
#A response to Pierce's challenge: construct a cellular automaton for which oscillators of all odd periods are possible, but for which no even-period oscillators exist.
#C, E, W, C'
@TABLE
n_states:4
neighborhood:oneDimensional
symmetries:none
var a = {0,1,2,3}
var b = a
1,2,0,3 #01210 → 03110
1,1,3,3 #03110 → 01310
1,0,3,3 #01310 → 01130
3,0,1,2 #01130 → 01120
1,2,1,2 #01120 → 01210
2,a,b,1
3,a,b,1

Test pattern:

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x = 7, y = 7, rule = Oddball
A$BA$B2A$B3A$B4A$B5A$B6A!

Posted: **April 29th, 2016, 9:27 pm**

Here's an 'oddball' rule with only three states:

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@RULE Oddball3State

A rule made to address the challenge of producing a rule which can only have oscillators of odd periods 
(but any odd period), using three states (including vacuum).

@TABLE
n_states:3
neighborhood:Moore
symmetries:none
var a = {0,1,2}
var b = {a}
var c = {a}
var d = {a}
var e = {a}
var f = {a}
var g = {a}
var h = {a}

0,0,0,1,0,0,0,0,0,1 #Move light particle left.
0,0,0,0,0,0,0,1,1,1 #Move heavy particle right.
0,0,0,0,0,0,1,1,0,1 #Move heavy particle right.
0,0,0,1,0,0,0,2,0,1 #Light particle can collide with wall.
0,0,0,0,0,1,2,0,0,1 #Grow a light particle on a left wall into a heavy particle.
0,0,0,2,0,0,0,1,1,1 #Bottom of heavy particle on right wall -> light particle.
1,0,0,0,0,0,0,2,0,1 #Grow a light particle on a left wall into a heavy particle.
1,a,b,c,d,e,f,g,h,0 #Kill all particles in other situations.

Example:

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x = 7, y = 13, rule = Oddball3State
B3$BA.B3$BA2.B3$BA3.B3$BA4.B!

Posted: **April 29th, 2016, 9:54 pm**

Sphenocorona wrote:Here's an 'oddball' rule with only three states:
Code: Select all
@RULE Oddball3State

A rule made to address the challenge of producing a rule which can only have oscillators of odd periods 
(but any odd period), using three states (including vacuum).

...

Wow! I like it! I had thought about the idea of using a "thin" signal one way and a "fat" signal the other way, but I couldn't figure out how to bound it properly.

Posted: **April 30th, 2016, 6:14 am**

3 states, 1-dimensional:

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@RULE Disparity
#C 3-state one-dimensional rule by Adam P. Goucher, in which
#C there exists a period-n oscillator if and only if n is odd
#C, W, E, C'
@TABLE
n_states:3
neighborhood:oneDimensional
symmetries:none
var a = {0,1,2}
var b = {0,1,2}
var c = {0,1,2}
2,1,a,2  # 12 is immortal
1,a,2,1  # 12 is immortal
0,1,2,0  # 102 disappears
2,2,0,1  # slow reflection
0,1,1,2  # fast reflection
0,a,2,2  # 2 moves left
0,1,a,1  # 1 moves right
a,b,c,0  # everything dies

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x = 10, y = 7, rule = Disparity
A2B.AB2$A2B2.AB2$AB.B2.AB2$AB5.BAB!

Proof: Since '12' forms an immortal wall, it suffices to consider minimal oscillators matching the regular expression '12.*12', where '12' never occurs within the 'active' region between the two walls. It is easy to see that the population can never increase from one generation to the next, so an oscillator must have constant population. Hence, '102' can never occur within the active region. It can thus be deduced that '10*2' never occurs within the active region, as it must eventually become either '12' or '102'.

Hence, a '2' can never appear to the right of a '1' in the active region. So any oscillator must have the form:

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12[02]*[01]*12

If the active region is non-empty, we can run the oscillator until the leftmost position is a '2' and the oscillator matches the following pattern:

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122[02]*[01]*12

Due to population conservation, the next digit must be a '0':

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1220[02]*[01]*12

In the next generation, the '2' becomes a '1'. This violates the 'no 10*2' rule unless there are no other '2's, and the oscillator must then have the form:

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12[01]*12

Moreover, we can deduce from population conservation that '11' may not appear, and from the 'no 10*2' rule that '1000*1' cannot appear either. Hence the oscillator must have the form:

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120*(10)*10*12

If there are more than three live active cells, the leftmost two will become '2's and eventually impact on the left wall to become a '12', contradiction. And if there are two active cells, they will diverge, ricochet, and recombine into a '12'; again, contradiction. So the only possible oscillators have the form:

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120*10*12

and are precisely the ones we need to generate every odd period. QED

Posted: **May 1st, 2016, 3:00 am**

I presume it would be similarly interesting to try and create rules where only even periods are possible (Which would mean period 1 is impossible; meaning B0, I guess. Would probably be harder than the odd period rules, but I am no authority of course)

But the reason I post here is because I want to know if anyone is willing to create the rule described here. I've written RLE functionality for my javascript app so I'd be able to load my creations in Golly if I only had a ruletable.

Posted: **May 1st, 2016, 10:06 am**

blah wrote:I presume it would be similarly interesting to try and create rules where only even periods are possible.

I'm pretty sure B345/S5 has that property, but I don't know if there's a proof.

Posted: **May 8th, 2016, 2:56 pm**

What about a rule that is not explosive, but has 2d replicator(s)?

Posted: **May 8th, 2016, 3:23 pm**

muzik wrote:What about a rule that is not explosive, but has 2d replicator(s)?

B2a/S is the best example of this. Unfortunately, variety is scarce

Posted: **May 8th, 2016, 5:06 pm**

drc wrote:
muzik wrote:What about a rule that is not explosive, but has 2d replicator(s)?
B2a/S is the best example of this. Unfortunately, variety is scarce

Rule table?

Also, the replicator in the thread is only 1d.

Posted: **May 15th, 2016, 8:22 am**

Well, anyone care to make me another mashup rule? This one's for highly Life related rules, usually with added quirks and stuff.

Rules:

Life - Green (0 255 0)

HighLife - Yellow (255 255 0)

tlife - Blue (0 0 255)

thighlife - Cyan (0 255 255)

DryLife (B37/S23) - Red (255 0 0)

B38/S23 - Magenta (255 0 255)

salad - Dark Green (0 127 0)

hlife3 - Olive (127 127 0)

alife - Dark Blue (0 0 127)

B34tw5y/S23 - Teal (0 127 127)

GlideLife - Crimson (127 0 0)

B35/S236 - Purple (127 0 127)

B3578/S23 - Orange (255 127 0)

EDIT: yes, it should probably have the same death conditions as Rainbow does

Posted: **May 20th, 2016, 2:22 pm**

Not to be rude, but I really want that^ rule asap.

If nobody has the time to make it themselves, can they at least try to teach me how to make them? Thanks

ConwayLife.com

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