ConwayLife.com

Posted: **August 4th, 2023, 11:09 pm**

This topic is about discussing explosive rules in general, so a pattern in an explosive rule, unless it is the smallest(or you think it is the smallest) exploding pattern of some kind of pattern

Here is my measure of how explosive the rule is:how long the shortest line that explodes
Under this measure, B3/S237 is more explosive than DotLife(B3/S023), which is more explosive than DryLife(B37/S23). B3/S237's 17 in a row is the shortest exploding line,DotLife's 23-in-a-row is the shortest exploding line, but DryLife doesn't have any exploding lines up to 54 in a rule. B3/S237c also doesn't have any explosive lines up to 54 in a row, so we aren't certain which is more explosive under this measure
Edit:B3/S237c's 64 in a rule is explosive
Edit:DryLife's smallest exploding row is a 93-in-a-row, making B3/S237c more explosive than DryLife

yujh wrote: ↑
August 4th, 2023, 11:54 pm

Disaster16439 wrote: ↑
August 4th, 2023, 11:42 pm
Doesn't that mean Live Free Or Die has a critical mass of 3? Also, critical mass is quite hard to measure, for DryLife critical mass would probably be around 7 or so(probably), and checking 2^49(minus symmetry) patterns won't be easy, that's 562,949,953,421,312 patterns(minus symmetry) to evolve!
drylife is 6.
Code: Select all
x = 3, y = 4, rule = B37/S23
o$2o$b2o$2bo!
(also i dont think this is threadworthy but i shouldn't complain)

Did you even read the measure? This is only one pattern, and one is less than 8388608(also I agree this isn't threadworthy can you ask moderators to move it to somewhere else? I don't know where to post it)(also I agree that my measure is a bad measure because 3-4-life is ∞

Posted: **August 4th, 2023, 11:29 pm**

I have a better metric for measuring how explosive a rule is: critical mass. The critical mass of a rule is the least integer n such that at least half of all patterns that fit in a n*n box exhibit quadratic growth. For example, Live Free or Die (B2/S0) has a critical mass of 2, as only 5 of the 16 different patterns in a 2x2 box explode (L-triomino in 4 orientations and O-tetriomino), while most patterms that fit in a 3x3 box explode.

Posted: **August 4th, 2023, 11:42 pm**

erictom333 wrote: ↑
August 4th, 2023, 11:29 pm
I have a better metric for measuring how explosive a rule is: critical mass. The critical mass of a rule is the least integer n such that at least half of all patterns that fit in a n*n box exhibit quadratic growth. For example, Live Free or Die (B2/S0) has a critical mass of 2, as only 5 of the 16 different patterns in a 2x2 box explode (L-triomino in 4 orientations and O-tetriomino), while most patterms that fit in a 3x3 box explode.

Doesn't that mean Live Free Or Die has a critical mass of 3? Also, critical mass is quite hard to measure, for DryLife critical mass would probably be around 7 or so(probably), and checking 2^49(minus symmetry) patterns won't be easy, that's 562,949,953,421,312 patterns(minus symmetry) to evolve!

Posted: **August 5th, 2023, 4:01 am**

So this means that B37/S23's critical mass is 6, B34/S23's critical mass is 4 and B1/S's critical mass is 1? Are double-digit critical masses possible?

Posted: **August 5th, 2023, 4:52 am**

Anyways, i think i would like to point out some edge cases, e.g. explosion due to symmetry.
without symmetry this rule is not explosive:

Code: Select all

x = 4, y = 1, rule = B3-q4ak/S23aeiy4aceit5eiy6ci7e8
4o!

not being a line (almost) always explode:

Code: Select all

x = 4, y = 1, rule = B2c3-i45/S2-i34
4o!

the second measurement has some minor problems (however this is rare enough you can just ignore it)
ruletable proof of concept:

Code: Select all

@RULE test-I


@TABLE

n_states:8
neighborhood:Moore
symmetries:permute
var a={0,1,2,3,4,5,6,7}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var z={1,2,3,4,5,6}
1,1,1,1,1,1,1,1,1,3
3,3,3,3,3,3,3,3,3,4
4,4,4,4,4,4,4,4,4,5
5,5,5,5,5,5,5,5,5,6
6,6,6,6,6,6,6,6,6,7
7,a,b,c,d,e,f,g,h,7
0,2,7,a,b,c,d,e,f,7
2,7,a,b,c,e,d,f,g,7
1,a,b,c,d,e,f,g,h,2
0,2,2,2,0,0,0,0,0,2
0,2,2,2,2,2,2,2,0,2
2,2,2,0,0,0,0,0,0,2
2,2,2,2,0,0,0,0,0,2
2,0,0,0,0,0,0,0,0,2
z,a,b,c,d,e,f,g,h,0

this rule is explosive, but a garden of eden can destruct the explosion, which will likely appear in a big soup, so for a large enough n*n box it is more likely not to explode, but for a smaller one it will.
this might be something similar, although it is based on very different mechanism

---------------------------------------

Some ways to eliminate the first problem is that we can just seperate rules that explodes on symmetry only from those thyat explodes without symmetry. I do not have any idea on how to deal with the second one.

Another way on how to mesure explosions would be the density of the explosion and the speed, but that does not tell how common explosions are and there are (might be, at least) rules that explodes with different speed(e.g. two explosive 2d faildrep with different speed) and density (e.g.uh int rules that only considers their diagonal neighbour, and what their orthogonal neighbours are does not matter. I'm slightly too stupid to construct one on the spot)

Posted: **August 5th, 2023, 7:18 am**

Haycat2009 wrote: ↑
August 5th, 2023, 4:01 am
So this means that B37/S23's critical mass is 6, B34/S23's critical mass is 4 and B1/S's critical mass is 1? Are double-digit critical masses possible?

No, don't you even read what it says? The stairstep hexomino is only one exploding pattern, not half of all patterns. Also even if they were all explosive, it would be 4 because it is contained in an nxn boundingbox. I don't know about b34s23 but b1s is 1. Also, I think we should develop a good amount of methods to use so in every case, we have a gpod method
I agree that my method is bad, B34ceity/S23 has a score of 61, which doesn't seem more explosive than B3/S237c. B37/S23 is about as stable as B37c/S23, which is about as stable as B3/S237c, but B37c/S23 has a score of 74. Seems fine, but DryLife seems a bit high

Posted: **August 7th, 2023, 2:48 am**

Disaster16439 wrote: ↑
August 4th, 2023, 11:42 pm

erictom333 wrote: ↑
August 4th, 2023, 11:29 pm
I have a better metric for measuring how explosive a rule is: critical mass. The critical mass of a rule is the least integer n such that at least half of all patterns that fit in a n*n box exhibit quadratic growth. For example, Live Free or Die (B2/S0) has a critical mass of 2, as only 5 of the 16 different patterns in a 2x2 box explode (L-triomino in 4 orientations and O-tetriomino), while most patterms that fit in a 3x3 box explode.
Doesn't that mean Live Free Or Die has a critical mass of 3? Also, critical mass is quite hard to measure, for DryLife critical mass would probably be around 7 or so(probably), and checking 2^49(minus symmetry) patterns won't be easy, that's 562,949,953,421,312 patterns(minus symmetry) to evolve!

My bad, LFOD has a critical mass of 3. To calculate the criticsl mass of a rule, instead of searching all n*n patterns it'd be easier to search, say, 1000 or 10000 n*n patterns. Someone could probably write a script for that.

Posted: **August 18th, 2023, 2:40 am**

B2ce/S1 is 5:

Code: Select all

# x: 8; rule: 1/2ce; step: 1;
# 1BG0
























x = 8, y = 3, rule = B2ce/S1
o5b2o$bo$o!

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