Nondeterministic rules ("Radiolife"?)

[primekitten]

If we change a standard cellular automaton so that after the transition is complete each alive cell has a very low probability of turning off then it might cause these changes (I didn't run any experiments but this is probably going to be the case when using a life-like rule):

1. Common simple things tend to break down after a while except some things like block don't usually break down as it takes multiple decays, since if one cell decays the rest collapse; in particular spaceships don't escape but rather have some probability of leaving a bit of debris.

2. Common growing structures (e.g. familiar 4's) are much more likely to be slightly changed at some point so they probably won't behave as expected; this might make more chaos than in the original rule.

3. If the probability is carefully balanced, perhaps common structures can produce enough chaos to refill the space with blocks and other debris while the debris doesn't thin out so quickly. Infinite growth may be possible with positive probability since if there is enough chaos and gliders produce some blocks far away from active regions, the pattern might grow infinitely past some bottleneck.

My question is: Could such a rule have interesting behaviour?

(Sorry if this is not in the right category or has already been considered, mods please move it if does not belong here)

[hotdogPi]

CGOL won't cause any interesting behavior here; it will decay to nothing. The most common cell decay that will not just turn to nothing or something less is the pond, which will become a honey farm if any cell is removed, but beehives can't turn into anything more. Long boats will turn into centuries, which has a larger envelope but still can't turn into anything if it settles. Toads into ponds is possible, but see above. Fleets and bakeries can cause chaos, but they're too rare. Everything else common (block, blinker, beehive, loaf, tub, boat, ship, barge) can't expand with one cell at a time removed. Blocks will take much longer to decay because it requires two at once, but they will eventually.

[confocaloid]

It could be fun to better understand consequences of introducing probability/randomness into a deterministic rule. The general idea was discussed before; see for example Interesting behaviour with probabilistic automata?, Making Cells Replicate/Move Randomly, Randomness in rules, Pseudorandom CA. One possibility is to run two parallel universes following two different rules, with states of cells in one universe used as a "background pseudorandom noise" to fine-tune evolution in another universe.

Edit: added a link.

[primekitten]

Code: Select all

import golly as g, random, time
const = {
    'B2n3-q4q5y6kn/S023-kq4c6i8':(0.0002,0)
}
rule = g.getrule()
if rule in const.keys():
    (c,d) = const[rule]
else:
    (c,d) = (0.001,0.05)
g.show(str(c) + ' ' + str(d))
while True:
    if g.empty():
        g.show('Life ended at generation ' + str(g.getgen()))
        break
    cells = g.getcells(g.getrect())
    n = len(cells)//2
    for i in range(n):
        if random.random() < c:
            g.setcell(cells[2*i],cells[2*i+1],0)
    g.step()
    g.update()
    time.sleep(d)

I ran this script on some soups in B2n3-q4q5y6kn/S023-kq4c6i8 (a rule by HotWheels9232 that normally explodes and leaves very dense clusters of still lives), with decay probability 1/5000; it seems to be rather stable, and in particular the still lives are very thin (mostly blocks and dots).

CGOL won't cause any interesting behavior here; it will decay to nothing.

I think it would make more sense to start with a rule that is sufficiently chaotic or even explosive, if the randomness is supposed to only remove cells. If the random decays were allowed to turn dead cells on it would create anything in the empty space unless we constrain the random cells, but then they can't affect the live cells.

[primekitten]

I ran a 60x60 radiolife soup on B3-ckq4q/S23-cey4i (rule by HotWheels9232) and decay probability 1/1000; after 48612 or so generations it stabilized with bounding box 1765/1541. The soup began in the western half of the southmost area, and only the upper right started expanding; it quickly grew to what became the center of the ash and also the south bump was formed. Then from the center it continued growing in all directions (forming this C shape) except the northwest was last; this area was also very explosive and stayed active for a long time, finally stopping slightly to the right of the initially small mess that made this entire region of ash. Some interesting still lives appeared. This rule seems reasonable for radiolife because a lot of common sequences are explosive but few actually cause linear or quadratic growth; in particular HotWheels9232 found a breeder that produces a lot of ash but it certainly cannot form when decaying is possible.

Radiolife B3-ckq4q/S23-cey4i 60x60 soup, generation 48612

shOosCt.png (90.34 KiB) Viewed 92 times

[breaker's glider gun]

from that pseudorandom CA link:

A small proof-of-concept for implementing randomness in CA. This is a lifeform that "feeds off" chaotic background noise (B24/S in this case), and can sustain a somewhat stable population:

Code: Select all

n_states:3
neighborhood:Moore
symmetries:permute

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}
var i = {0,1}
var j = {i}
var k = {i}
var l = {i}
var m = {i}
var n = {i}

#Growth into solid background
2,1,1,1,1,2,2,a,b,1
2,1,1,1,2,2,2,a,b,1
2,1,1,2,2,2,2,a,b,1

#Shift along solid edges
2,1,1,1,2,2,2,0,0,1
2,1,1,2,2,2,0,0,0,1

#Death by isolation
1,i,0,0,0,0,0,0,0,0

#Death by overpopulation
1,1,1,1,1,1,a,b,c,0
1,1,1,1,1,2,2,0,0,0

#B24/S background
0,2,2,i,j,k,l,m,n,2
0,2,2,2,2,k,l,m,n,2
2,a,b,c,d,e,f,g,h,0

Code: Select all

color=0		0	0	0
color=1		255	0	0
color=2		0	0	64

Here's an example pattern that survives some 6K generations:

Code: Select all

x = 8, y = 8, rule = brownian:T100,100
2A$2A$2.A$3.A$4.2A$4.2A2$5.3B!

Code: Select all

x = 102, y = 102, rule = brownian:T100,100
$5.2B.2AB.A3.2A2B.3A4.B2.B3.3BABA.2B.2B.3B2.5B10.B.B2.B.B2.A.A2.B2.B.
BA5.B2A2.B$4.B2.BA4.A2.AB3.A8.B5.B2.2A4.B.B.A.A8.B4.B5.2B5.2A2.B3.2B2A
4.B$2.2B2.B3.B.A5.B.B.B5.B14.B2.AB.A.2A2B2.B.2B.2B4.B.B4.B.A6.2B3.A.2A
.B.B2.B$2.B9.A3.3B.B.B8.3B3.2B3.B2.2A.A.B.B.4B5.B2.2B2.B6.2A.B3.2A.2B
2.2A.B$.BA.2B.2B.BA2.A4.4B.2A.3B3.2B3.B.B.B.B3.2A2.B.2B.B5.B4.B2.B2.B
.2A6.A.A5.B.2B$3.2B.B2.B2.2AB6.B2.A.B.2A.B4.B.B.4AB3AB2.B3.B.B2.B7.2B
5.A4.B.B2A.A5.BA3.2B$2.B9.2B2.B.2B2.B2.B.BA.B.A.B.B.B.A3.A5.B4.B2.2B2.
2B.3B2.B3.2BAB.3BA3.A7.A4.B$10.B.B2.B8.3B.4A.AB.2B4.3B4.4B3.B2.2B3.B2.
B.B5.A7.3A.2A.B.A.A3B$4.B3.B3.B.B.B6.B4.B4.2A5.B8.2B.B10.2B2.B.B.B2.A
2B3.4B.A.A.B2.AB4.B$.B2.2B5.B.B2.B4.2B2.B3.2A.A2.AB4.2B3.B4.B.B13.5B6.
B6.BA.B4.B.B.3B$.B3.B8.2B.B2.2A.A2.B.B.A2.2A.B4.B2.B9.B7.2B3.2B.B2.B.
B.2B.A.B2.B.A2.A2B4.B.B$5.B3.4B3.B2.BA.A6.2A2.A.B8.3B2.B.B3.B2.B12.B4.
B2.A3.3B2A2.A.B.2B3.2B$3.B.B.B8.B.B2.A11.A.3B4.B5.B5.B.B4.2B2.B3.B8.B
2A2.B.2B.A3.B.BA4.B$.B.B.B2.B.3B3.B7.2B3.4A2.2B4.B2.B2.2B3.2B2.2B.2B2.
B6.B3.3B5.B2.B2.A4.B.BAB$3.2B.2B3.B.2B3.2B3.B5.A2.A9.B.2B3A2.B3.2B2.B
.2B.2B2.B3.2B4.4B3.B8.B.2A$8.B3.B12.B4.B5.AB3.B4.A.A2.B5.2B2.2B.B4.6B
4.B3.B.B2.B5.B2.3B$.B.B.B2.B.3B6.B2.B5.B.B.B9.B2.B3.B.B3.2B4.B2.B2.B9.
B.B7.B6.B$.B.B2.3B5.B4.B6.A2.3B9.B.B.B2.B.3B3.B.B2.3B2.B4.BA3.2B6.B8.
2B$.5B5.2B2.B3.B3.BA.2AB.B.B.B4.B.B3.B.2B.B8.B.B.B2.B6.A.A.A2.A.AB4.3B
$.2B3.B4.B3.B4.B.B.2A2.2AB9.3B6.B14.2B8.A.A.A.2A3.2B5.B4.B$.2B9.B7.B.
2B.A.2A4.5B12.2B4.B3.2B2.B2.B5.2A.A2.A2.AB11.2B$7.2B2AB3.B15.A.B.2B.B
2.B11.A3.3B2.2B2.B7.BAB2A.2A2.A6.2B6.2B$4.B.B2.A3.B2.B.2B2.B3.2A3.2A2B
.2B2.2B9.2A.2A9.B4.BA5.B2.A2.A.A4.B2.B3.B$2.B.B.2BA6.B3.2B4.B.A3.A2.B
.6B5.B2.B.A.AB.B3.B.B.B3.2A4.B3.A2.A3.A2.B2.2B3.B.2B$2.B.B3.2A2.B2.3B
3.B3.B.A2.A3.B8.B.B.2B4.A3.B3.2AB4.A4.3B.3B2A.3A7.B2.B.A$.2A2.B2.A8.B
3.2B2.B2A3.A2.AB3.2B3.B2.B4.B3.B3.ABAB5.A.B3.B3.2A.A3.2A3.B.AB2.4A$.A
.B8.4B3.B.2B.B5.A.ABAB.B.B4.B5.4B3.B3.B.B.B2A2.B.2B2.B2A7.A3.B2.2B.BA
$2.AB6.2A3.B.B.2B3.B4.2A2.A2.3BA4B3.B2.2B3.3B4.A.2A2.2AB5.2A3.B.B2.2A
.B3.4A$.A8.A4.B2.B5.B3.A2.A3.B2.B4.B.B.B3.B2.2B3.2BA.AB.2B.B3.B.2B.B3.
B.B4.2A.BA2.A3.A$.A6.B.B.B.2B2.B6.B.A2.AB.2B3A5.B.B2.B.B5.B3.B3.B.2B4.
2B.B11.2B.AB3.2A2.A$10.B10.B.B4.3A2.B2.A2.B13.2B3.3B4.B.ABA3.B.2B2AB5.
2B.2A.B5.2A$6.B2.B2.A2.A2B.B.2B15.3B.B2.B4.B7.B5.2B3.2AB2.B.A2.A2.3B.
B2.A2.B.2B.A$7.B2.B.B2A2B.B.2B6.B2.A.3A.A2B3.B4.B2.B2.B3.B7.B.B.A.BAB
2.A3B.B3.B6.B4.A$3.A2.B4.B.A7.B6.B.B2A2.A.A4.B4.2B.2B3.2B2.B9.B.B2.4A
2.B2.B5.2B3.B3.A$.3A2.2B.B7.B4.B2.B.2A.A.B7.B5.B.2B3.B2.B.B.B.2A2.B2.
B4.A2.B2.2B14.A2.A$5.B.B5.B3.B4.B5.2A2.2B2.3B5.2B9.3B3.2A4.2B6.2B9.B3.
B4.B2A2.A$.A3.B5.B.B.2B6.A.A7.B.B.B2.2B4.B5.B2.B.B2.A2.A2.2A4.2B.B8.B
7.3B.A.A$.B2.B.2B4.AB2.B7.2A.B2.A3.B.2B3.2B3.B4.B3.B3.2A.A.2A.A2.AB3.
B4.B.B2.B5.B3.B3.B$8.2B3.B5.B.2B.A7.B2.B5.2B15.B2.2BA.B6.B.B.B.B2.2B14.
B$4.2B3.B.B2.B2.B.B12.B.B3.B4.3B2.3B.2B3.B6.2A.B7.B.4B5.B.B10.B$9.B2.
2B.B.3B2.B3.B3.B2.2B10.4B.4B.B3.B3.A2.2A2B.B3.2B2.5B2.B2.B8.2B$6.B2.2B
.B2.B.B.B3.3B.2B2.B2.B3.3B.B2.B4.2B3.B6.A4.A.B.B9.B.B9.B3.B2.B$10.B9.
3B6.B4.B.B.B2.2B5.B5.B.B2.B.2BA3.AB2.2B3.B2.B8.2B4.B.B.2B$3.B2.B2.B.B
2.B.B.2B4.B2.3B4.B.B.B5.B.B.B3.2B2.2B.2B.B2.B2.B.B4.B3.B4.B.B10.B2.B$
3.B8.B.B5.B4.2B8.2B3.B7.B.B2.5B2.B3.3B2.B2.B3.B3.B3.B.2B2.B2.B$4.B3.3B
5.B6.B.3B2.B8.2B.B.2B2.B.B2.B2.B8.B2.2B2.3B2.B2.B.B.B8.B.B.B$5.B6.2B.
B8.2B.2B6.B.B10.B5.2B6.B12.B8.B2.B3.B2.2B.B.B$2.2B2.3B5.B6.2B3.B2.B8.
B.B3.2B5.B5.B.B4.2B2.B2.B5.3B.2B.B.B4.3B5.2B$6.B2.B3.3B8.B6.B.2B5.B.B
.B2.2B2.B3.B3.B2.B5.2B.B2.B.B2.B4.B3.2B3.B2.2B$.4B.2B2.B4.B3.B.B2.B2.
B.B2.B.B2.2B2.B.B.B.3B6.B.2B5.B4.B.B.B2.A4.2B4.B3.3B4.B$3.B4.B2.3B11.
B2.B11.B2.3B.B9.B2.B4.3B.B3.B2.ABAB2A.B4.3B7.B$3.B.2B3.B5.B.B6.B2.B3.
B2.B3.B.B6.B.2B.B3.B5.B4.B6.A.2A.A.B7.2B.B.B$2.B4.B9.A.B5.B9.2B.B6.7B
.B3.B3.B3.B3.2B.B.A.A6.A2.A2.B$2.B4.B6.3A.A4.B.2B.B.B6.B3.B2.2B6.2B3.
3B.B5.2B2.2A.A.2BA.2A.3A3.B.B2.2B4.B$5.B6.2A.2A.AB.B2.2B.B.2B6.B.B8.B
.2B5.B3.2B2.B2.2B2.2A.B2.2A2.A3B4.4B.3B.B$2.2B.B6.BAB2.2BA3B.B4.B10.B
.B4.B5.B.2B2.B8.B.3B.A2.2B.A4.B2.B3.B5.2B$2.B9.A.B3.2A.B6.B.B6.B4.2B.
B.B3.B.B3.B2.5B.B.B.B.2AB5.A.2B2.2B6.B3.B$3.B9.A.B.B3.B2.3B3.B5.B7.B9.
4B2.B3.B.B5.AB.3B.A.A7.2B.BA4B.B$11.B4.2A2.A.B2.B.B19.B.B3.B.B3.B2.B3.
B.AB2.B2.3A.2A2.AB3.2B2.3A.B.2B$.B.B.B7.2A.A.A.2A4.B3.2B3.B5.B4.B11.B
6.B2A.A.B3.A2.A3.2A.A6.A.B4.2B$2.2B2.B.B5.A2.A5.B6.B4.2B4.3B.2B4.B4.4B
.B.2B2.2A.A5.2AB.B2.A.2AB2.3BA.B3.A$.AB6.BA.B2.3B5.3B4.B.B.2B9.B5.B3.
B3.B5.2B4.A4.AB5.A3.2A2.A.2AB.2B2A$5.B3.B2A.2B4.2A3.B.B3.B.B3.4B2.2B3.
B.B3.AB.B.B5.B5.B3.B.B.B.2B.2A4.2A.A.B4.B$.2A2.B.2ABA3.B2.B.2A3.B2.B2.
4B6.B.B4.B.B.B5.2A.B.B7.B.2B.3B10.B2.A.AB2.B$.2A2.B2.A.B5.2B8.B2.B7.3B
.B2.B3.B3.3A.B.2A2.2B3.3B.B4.B7.B8.2A3.A.A$.AB5.A3.B3.2B9.2B.B.2B4.B.
B3.2B3.2B.2B4.A15.2B14.2B2.A2.A.2A$4.AB.AB.B.B7.B11.2A3.B3.B2.B3.2B3.
B2.A2.2A3.B.2B2.B2.B2.B2.B3.B8.A.A.A3.A$3.B2.2AB2A.B3.B2.B2.3B4.A3.2A
2.B13.B2A.A.A2.2A7.B4.B3.B.B4.B.B4.A.BA.2A$.B4.2B.B.A.B5.B.B3.2B2.5A7.
B.B5.B.B2A.A2.A3.2B5.B2.B2.B.B12.B3.2A2B.A$2.4B3.2A2B.B.2B5.B5.B.AB8.
B9.B4.2A2.B.B5.B2.2B7.B2.B3.B3.B7.2A$.A7.BA.B5.B4.B.B2.2B3.B5.B.B3.3B
4.B2A3.A.B.B6.B14.B4.2B4.2B$2.B.B2.B4.B.B3.B.B.B.B2.B13.B.3B.B4.2A3.A
2.3B9.2B11.B6.B3.A2B2A$.A2.B.2B6.B3.B7.2B3.B9.B7.2B3.2B2.B.B2.2B.B.B5.
2B2.2B7.2B2.B3.A3.A$4.2B2.B5.B4.B.2B6.2B2.B3.B5.B8.2B15.B2.B3.3B6.B3.
B2.B2.BA.A.A$6.B.2B5.B11.B9.B3.B6.AB2.B7.B2.2B.B9.B7.B.2B2.B4.B.A$2.B
.B.2B11.2B12.4B10.B3.3A2B.B11.B5.B.B.2B.B2.B2.B2.B.B.B$.B4.B5.B.B.2B.
B5.2B2.B.2B3.B11.B.A.A.AB2.2B2.4B4.B.B7.3B4.2B6.B4.B$3.B2.B2.B3.2B5.B
.2B2.2B2.2B.5B3.B.B2.B3.A2B.A.B.2B4.B11.B.B.A.2B.2B2.AB2.B4.B.B$10.2B
6.B5.B2.3B3.B2.B2.A7.2B5.AB.2B8.3B2.B.A2B.B2A4.B.2BAB3.B.B3.B$5.B.B2.
B3.B9.B5.B.B.B.A.B7.B2.3B6.B8.B6.2A.2B3.2B2.B3.B8.AB$.A.A.B3.B5.B2.B4.
B2.B4.B2.BABA4.B4.B.B3.B.B.2B.2A2.B.B6.A2.B3.B.AB6.2B4.A.B$2.A.A2.B8.
B.2B2.B3.A.B5.B.A5.B3.5B9.A2BA10.3A2B3.3B2.B6.B2A.B2A$3.AB.B5.B3.2B.3B
2.B.A.B5.B3.2B.B.B4.B.B.B.B3.B2A.2A.B3.2A4.A4.B2.2B3.B2.2B.B.B.A$3.AB
2.B.2B4.B.B6.B2A.B.B3.B4.B4.B.B.B4.B.B.2BA2.A2.B2.2A2.A3.A4.2B6.2B2.B
2.A.B2A$3.B2.A.B.2B.B4.5B3.2AB.B.B3.B4.B.B.B8.A.2B2.B8.B.2A3.A.2B11.4A
4.A$.A.B2.B9.B3.B.B.B2.B.B.B3.2B6.2B5.BA.B2A3.B4.B2.B2.A6.A3.B3.4B2.2A
4.2B$.A.2B3.B2.B2.B4.B5.A2B.B2.B4.B.B.B4.B2.A.2A.B2.B2.B3.B3.B3.2A3.A
.A.B.B4.2B3.2B5.A$3.A5.2B3.2B2.B2.B3.A4.3B5.B.B.B2A2.BA2.B2.B.B3.2B.2B
2A.B3A2.2A.3A.2AB4.B3.B2.B3.A$.2B2A.2B2.A6.B2.2B5.A4.B2.2B2.2B.BA3.B3.
B2.B2A3.B2.BA.A9.A3.A4.2B.2B3.2B.B.A$3.A.B3.2A.3BA.B3.B.B2A.B6.B.B4.B
7.2B4.A.A.B2.B5.3B.2B3.A.A.A5.2B2.B7.2A$4.B6.A2.2A2.B.B2.2A2.B4.2B.B7.
B6.B5.A.B2.B3A3.B.2B2.3A.A.A18.AB$.B2.2B.B4.2A2.B.2B2.B2.2A5.B5.2AB4.
B.B2.2B.A8.A8.2AB.A3.A2.B$.3B7.A2.3A6.A3.A2B5.2BA.AB6.B2.B4.A2.2B.B.4B
.AB.A.A.A.2A5.AB2.B4.2B.B.B.B$4.3B2.2A.A5.B.B.3ABA3.B.B2.B2.A3.2B2.2B
.2B3.2A8.B3.A.A2.2A3.A5.2A3B2.B4.B$2.B.A3.A2.A.A.B5.A4.BA.A4.2B3.B3.B
.B.2B2.B3.A4B2.B.A.B.A2.2A2.2A2.AB.BA.A2.3B2.3B$2.B.A2BA.A3.A2.B5.2A2.
B.2A.B.B3.B2.B.B.2A2.3B.B.B.A3.A.B.2AB.B.A2.2A2.2A.B.A.AB.AB3.B.B4.B$
.B.2A.B.2A.A.2A3.B5.A.B2.A.AB4.B.AB2.A2.B2.B.B.2A.2A.A4.AB.B.B2.A2.A2.
AB2.BAB.A2.AB4.B$6.B.A2.2A.B2.B.2A2.A.A4.3A2.B2.A.A3.B.AB3.BA4B3.A3.B
.B6.A.A5.B4.BA4.AB.BAB2.B$.B8.A3.B.2B.A.2A.2A3.AB.B4.AB.3A.A3.B4.AB3.
A.2A2.2B4.B3.A.A6.B.B.2A2.2A3.A$4.B5.B2A4.A2.A3.A5.A.B.B3.A2.2AB10.B4.
A4.2B5.B3.A.A.A5.B2.B.2A4.A.B!