IceNine

[Alexey_Nigin]

IceNine is a pattern that grows quadratically, consuming all random ash around it. Any class-3 explosion fits the definition. For a more interesting example, run a random seed in B25678/S5678.

What is more funny, however, is this post by Adam describing an IceNine in Conway's Life. Given that GoL is quite a stable automaton, the post looks like a joke, and Adam later confirmed this.

So, Dave, could you explain how you came up with the idea of massive (although successful) prank which ran many people into believing that Life is class-3 on large scale?

[dvgrn]

What is more funny, however, is this post by Adam describing an IceNine in Conway's Life. Given that GoL is quite a stable automaton, the post looks like a joke, and Adam later confirmed this.

So, Dave, could you explain how you came up with the idea of massive (although successful) prank which ran many people into believing that Life is class-3 on large scale?

It was certainly never intended to be taken seriously, and I don't think that belief in IceNine actually traveled very far. The exceptions might be a few people who didn't read all of the message, which was maybe a little too long-winded... but it did include the following paragraph (minus the helpful link):

And before you all ask, my alternate-universe oscilloscope was repossessed by the Outsiders the other day, so unfortunately I can't lend it out. But there didn't seem to be anything but IceNine out there anyway --

This was all a part of a longer discussion on open problems in Conway's Life -- in particular, whether it might be possible to complete a proof that indestructible B3/S23 patterns do not exist.

My intended point was just that any proof would have to definitely rule out surprising behavior that might appear only on a macro scale, such as a huge quasicrystalline agar that only appears on scales larger than we can currently simulate. Kind of like the seeds for spiral demons in a cyclic CA rule, maybe: if there are a lot of states in the cycle, spiral seeds are unlikely to appear at all in small areas, but the odds increase to near unity as the size of the simulation passes some inevitable statistical threshold -- and once those spirals get started they take over, like a Langton's Ant highway.

How do you absolutely prove that there isn't something analogous in Conway's Life? It could be a self-reinforcing "natural" agar that outcompetes everything else, but needs an initial soup thousands of cells on a side to get started. Catagolue will never see it, any more than it would see a spiral seed if it were running 16x16 soups with a 999-state cyclic CA.

I absolutely agree that it's very hard to seriously argue that an indestructible B3/S23 pattern might actually exist, but it's even harder to argue that a proof of nonexistence might be within easy reach...!

Here's a little more context for Adam's quotation:

Re: Open problems in Conway's Life -- indestructible patterns
Date: Fri Feb 22, 2008

--- Brice Due wrote:
>> Prove that, for any stable pattern, there exists a sequence of
>> gliders that interact with it leaving zero live cells.
>
> [T]his one seems like it will need to be solved by induction and contradiction...
> There would be several prongs to such a proof. One might classify all
> possible edge and corner interactions a glider might have with local
> subsets of the pattern. The aim would be to show that all possible
> collisions result in erosion of the pattern.

Can't resist playing devil's advocate for a while on some of these speculations. At least at first glance, this initial line of investigation doesn't look too promising, just because erosion is so far from being inevitable. Even for stable patterns, eaters and boat-bit catchers are fairly common, and even rarer kinds of accretion are possible:

Code: Select all

#C glider eater/catcher (boat-bit, beehive, and block)
#C Based on Koenig's 16.1262 -> 22.475646 in collision table:
#C http://pentadecathlon.com/lifeNews/2008/02/glider_collisions_with_16_bit.html
x = 22, y = 20, rule = B3/S23
7boo$6bobbo$7boobboo$9boobobboo$5b4o6bobo$4bo3bo6bo$4boo$19boo$boo16bo
bo$obo16bo$bbo$8boo$8bobo7boo$8bo9bobo$18bo3$8boo$8bobo$8bo!

I'm guessing the glider-to-beehive "rock" reaction must be old and well-known, by the way? Don't think I've run into it in LifeLine or in the archives. Seems unusual to be able to add six cells with one glider:

Code: Select all

x = 11, y = 11, rule = LifeHistory
3.C$2.C.C$3.C2.2C$4.2C.C$.3C$C2.C.2D$2C2.D2.D$5.2D$8.3A$8.A$9.A!
#C [[ THUMBNAIL ]]

Gliders on other nearby lanes cause the usual deadly explosions, of course, and any resulting random ash is usually sparse enough to be trivially cleaned up one object at a time. Someday an exhaustive search might be able to put a limit on the number of adjacent glider lanes that a stable object can absorb input on and recover within N ticks -- say, 14 ticks, when another glider might be coming along? I always thought the eater2's four adjacent lanes were fairly impressive... but looking at "Dean's Eaters" from a decade ago always gives me the uneasy feeling that the search space is mind-bogglingly large and you never know what someone might find in it.

> Another prong could be an informatics approach. Given all the
> collective experience with patterns vs glider guns, it is intuitively
> obvious that no non-self-repairing pattern can ever resist an infinite
> number of gliders.

Aha! You and your intuition have clearly not been exposed to the IceNine Agar, found recently with an alternate-universe oscilloscope:

Code: Select all

#C IceNine seed -- currently this is the smallest sample
#C for which no external conditions have yet been found
#C that prevent long-term quadratic growth
x = 2718, y = 4669, rule = B3/S23
<<<Server notice from fermat.yahoo.com:
11.9MB nonstandard text removed from message
Please notify sender of potential virus threat>>>

...

> So such a non-destructable pattern would have to contain stored
> information about [its] own structure. Forget about the problems of
> reading out and acting on that information for a moment. This prong
> of the proof could simply calculate the theoretical minimum cells per
> bit of structural information, and the minimum area per bit, and then
> show that for a given size and complexity of pattern, the required
> memory is greater than the pattern itself. Proof by reduction to
> absurdity. This prong might be enough to prove the theorem, if only
> someone could make the genius leap of proving that only
> indestructable self-referential patterns can possibly be
> counterexamples.

Can't tackle this part until IceNine is proven not to exist, then. I think you also get into thorny issues here with encoding and decoding schemes, which could be quite efficient if the right Conway-space mechanisms were found. For a proof you'd have to be able to rule out arbitrarily large enclosed spaces containing mechanisms that maintain many copies of the same boundary-wall segment.

> Another prong could tackle the mechanistic requirements of such a
> self-repairing pattern. We have quite a bit of knowledge about how
> static and dynamic patterns can be incrementally constructed from
> gliders. However many of these constructions require glider access
> from all directions. If you assume a non-destructable pattern exists,
> it will have a definite area with a definite inside and outside. Repair of
> patterns at the border will require constructions utilizing only gliders
> from the interior directions. "Flying fortress" patterns would have
> similar restrictions on self repair mechanisms.

We can dispose of the idea of invulnerable flying fortresses, at least, just by sending two of them on a collision path. I think this approach does point out the basic implausibility of self-repairing patterns -- at least ones that can fend off any and all attackers, even malevolent omnicient glider-fleet designers.

Might be more of a problem of information flow than information storage. Let's see: chaos can, and very often does, spread at close to lightspeed. Warning signals from disruption detectors could theoretically travel at lightspeed but will be slower in practice. Self-repair of damaged patterns can't happen anywhere near lightspeed.
So detecting and repairing a problem once it gets started seems pretty hopeless, if you're using a central database. Just have to put up firewalls and wait until the problem burns itself out -- and rebuild very slowly, if at all.

> By enumeration, all the known active primitives (herschels, etc) can be
> shown to be always vulnerable to gliders. If it can be proved that all
> chaotic sub-patterns eventually settle to a local combination of ash and
> known active primitives, then a proof by induction may be possible on
> the larger pattern as a whole. Combined with the ash reduction prong,
> this could cover all the bases.

Hmm -- but one open problem that may be within reach of a proof is that, given a large enough construction area, anything glider-constructible is also slow-glider-constructible (and therefore constructible by "chaotic sub-patterns", with very low probability). So the above "if" looks like a mighty big one: wouldn't you have to enumerate all, or nearly all, glider-constructible patterns?

[praosylen]

Hmm -- but one open problem that may be within reach of a proof is that, given a large enough construction area, anything glider-constructible is also slow-glider-constructible (and therefore constructible by "chaotic sub-patterns", with very low probability). So the above "if" looks like a mighty big one: wouldn't you have to enumerate all, or nearly all, glider-constructible patterns?

Although this is a bit off topic, hasn't that last problem been solved by the block-and-clock inserter, or am I missing something?

About the issue of IceNine: I would say that it is probably impossible for such a pattern to exist. Such a pattern, if it exists, would probably not be a true agar; it should be composed of smaller subunits in order to prevent decay propagating uncontrolled into the interior. It seems near impossible for it to automatically generate the structures reconstruct itself upon impact, and to prevent a collision with a non-blonk generating the same non-blonk in a closer location. Assuming that it repeatedly domino-sparks at its leading edge (the most plausible method I have come up with of deleting all blonks it encounters), the following reactions could mess it up severely:

Code: Select all

x = 51, y = 9, rule = B3/S23
$bo16bo$obo14bobo26b2o$obo14bo2bo25bobo$bo16b2o27b2o2$2b2o16b2o23b2o!

And then there is the question of the corners. Surely it should be difficult, if not impossible, to merge a component that domino-sparks a whole region in front of it with one that dot-sparks at the corner without leaving more than a two-cell gap (which a blinker could slip through):

Code: Select all

x = 67, y = 21, rule = B3/S23
2o15b2o13b2o16b2o12b2o$2o15b2o13b2o16b2o12b2o2$3b2o14b2o12b2o15b2o11b
2o$2b5o11b5o9b5o12b5o8b5o$2b5o11b5o9b5o12b5o8b5o$3b2o14b2o12b2o15b2o
11b2o$3b2o14b2o12b2o15b2o11b2o5$bo14bo$bo14bo$bo14bo2$2b2o10b2o$b5o7b
5o$b5o7b5o$2b2o10b2o$2b2o10b2o!

Code: Select all

x = 7, y = 5, rule = B3/S23
3bo$3bo$3bo2$2o3b2o!

Not to mention that the dot-spark corner only deletes two out of every five blinkers (it turns the rest into beehives), and it can't even reach the rightmost three blocks. I'm sure that a more efficient mechanism could be found, but the same problems would be inherent in each one. And then, there is still the issue of having it decompose into only blonks when breached. I could see a way where the most common signal propagation through an agar could produce only blonks, but what about the external mess? It seems almost inevitable that it will produce more non-blonks further towards the center of the IceNine than the original one that caused the problem.

I could still see some large engineered pattern that can probe debris by shooting a glider at it, but there is the problem mentioned about the information content of the pattern. It does seem that the information required to delete the surrounding agar goes up with the first power of the radius, but the storage capacity goes up as r^2... maybe it might work. However, what does happen if it finds another such pattern? Maybe it should try to merge with it; but the information requirements would be quite large. Needless to say, such a pattern would have to be amazingly huge. I can't rule out the possibility of such a pattern, but I don't think we'll see one made during my lifetime... at least before 2050. I have thought of taking the first steps in that direction by making a device that can heisenburp a block anywhere within a certain region (by scanning with this reaction):

Code: Select all

x = 4, y = 5, rule = B3/S23
obo$bo2$2b2o$2b2o!

But I don't see any way to generalize this to more than two different types of debris (as this reaction can liberate a glider in conjunction with the previous reaction, and the previous reaction leaves a boat untouched):

Code: Select all

x = 4, y = 6, rule = B3/S23
2bo$2o2$2bo$bobo$2b2o!

[dvgrn]

Although this is a bit off topic, hasn't that last problem been solved by the block-and-clock inserter, or am I missing something?

That's right. That whole discussion is from back in 1 B.C. (Before Conwaylife.com). Quite a few things in Life have gotten easier since then.

About the issue of IceNine: I would say that it is probably impossible for such a pattern to exist...

Yes. What you've written is a good summary of several of the reasons why no one should bother looking for a real-Life indestructible pattern. The idea behind IceNine was the claim that it's also a waste of time to try to prove formally that indestructible B3/S23 patterns don't exist.

They pretty obviously don't exist, but actually proving it is a seriously intractable problem. People's arguments against indestructibility generally seem to appeal to intuition -- which is often a good guide. But very occasionally, depending on the rule, intuition misfires when you're moving from micro-scale behavior to huge macro-scale patterns. In any formal proof, you'd have to account for extraordinarily unlikely coincidences in macro-scale patterns... and there are a lot of macro-scale patterns out there.

I really liked my far-fetched analogy to cyclic CAs, some of which have indestructible patterns that are ridiculously unlikely to occur on a small scale, but certain to occur in an infinite random universe. A cyclic CA with a million states would never spawn a demon spiral in any reasonable soup experiment. But any intuition that people might develop by watching cyclic-CA soups would be worse than useless, because in that case the indestructible patterns are actually out there.

The hypothetical IceNine case would be a high-period agar that just happens to naturally throw off frothy sparks around its edges that die back in the same way no matter how they're perturbed, and destroy whatever they hit, or at least reduce it into something slightly simpler and easier to digest on average. It would certainly be proof of an Intelligent Designer with a very scary nerdy sense of humor.

By contrast, an indestructible demon-spiral pattern in a million-state cyclic CA is trivial to construct, once you know how it works. It's just that the smallest ones can't be packed any smaller than a 1000x1000 bounding box.

[Alexey_Nigin]

I really liked my far-fetched analogy to cyclic CAs

I also liked it, so here is a rule file:

Code: Select all

@RULE Cyclic256

@TABLE

n_states:256
neighborhood:Moore
symmetries:permute

var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}

0,1,a,b,c,d,e,f,g,1
1,2,a,b,c,d,e,f,g,2
2,3,a,b,c,d,e,f,g,3
3,4,a,b,c,d,e,f,g,4
4,5,a,b,c,d,e,f,g,5
5,6,a,b,c,d,e,f,g,6
6,7,a,b,c,d,e,f,g,7
7,8,a,b,c,d,e,f,g,8
8,9,a,b,c,d,e,f,g,9
9,10,a,b,c,d,e,f,g,10
10,11,a,b,c,d,e,f,g,11
11,12,a,b,c,d,e,f,g,12
12,13,a,b,c,d,e,f,g,13
13,14,a,b,c,d,e,f,g,14
14,15,a,b,c,d,e,f,g,15
15,16,a,b,c,d,e,f,g,16
16,17,a,b,c,d,e,f,g,17
17,18,a,b,c,d,e,f,g,18
18,19,a,b,c,d,e,f,g,19
19,20,a,b,c,d,e,f,g,20
20,21,a,b,c,d,e,f,g,21
21,22,a,b,c,d,e,f,g,22
22,23,a,b,c,d,e,f,g,23
23,24,a,b,c,d,e,f,g,24
24,25,a,b,c,d,e,f,g,25
25,26,a,b,c,d,e,f,g,26
26,27,a,b,c,d,e,f,g,27
27,28,a,b,c,d,e,f,g,28
28,29,a,b,c,d,e,f,g,29
29,30,a,b,c,d,e,f,g,30
30,31,a,b,c,d,e,f,g,31
31,32,a,b,c,d,e,f,g,32
32,33,a,b,c,d,e,f,g,33
33,34,a,b,c,d,e,f,g,34
34,35,a,b,c,d,e,f,g,35
35,36,a,b,c,d,e,f,g,36
36,37,a,b,c,d,e,f,g,37
37,38,a,b,c,d,e,f,g,38
38,39,a,b,c,d,e,f,g,39
39,40,a,b,c,d,e,f,g,40
40,41,a,b,c,d,e,f,g,41
41,42,a,b,c,d,e,f,g,42
42,43,a,b,c,d,e,f,g,43
43,44,a,b,c,d,e,f,g,44
44,45,a,b,c,d,e,f,g,45
45,46,a,b,c,d,e,f,g,46
46,47,a,b,c,d,e,f,g,47
47,48,a,b,c,d,e,f,g,48
48,49,a,b,c,d,e,f,g,49
49,50,a,b,c,d,e,f,g,50
50,51,a,b,c,d,e,f,g,51
51,52,a,b,c,d,e,f,g,52
52,53,a,b,c,d,e,f,g,53
53,54,a,b,c,d,e,f,g,54
54,55,a,b,c,d,e,f,g,55
55,56,a,b,c,d,e,f,g,56
56,57,a,b,c,d,e,f,g,57
57,58,a,b,c,d,e,f,g,58
58,59,a,b,c,d,e,f,g,59
59,60,a,b,c,d,e,f,g,60
60,61,a,b,c,d,e,f,g,61
61,62,a,b,c,d,e,f,g,62
62,63,a,b,c,d,e,f,g,63
63,64,a,b,c,d,e,f,g,64
64,65,a,b,c,d,e,f,g,65
65,66,a,b,c,d,e,f,g,66
66,67,a,b,c,d,e,f,g,67
67,68,a,b,c,d,e,f,g,68
68,69,a,b,c,d,e,f,g,69
69,70,a,b,c,d,e,f,g,70
70,71,a,b,c,d,e,f,g,71
71,72,a,b,c,d,e,f,g,72
72,73,a,b,c,d,e,f,g,73
73,74,a,b,c,d,e,f,g,74
74,75,a,b,c,d,e,f,g,75
75,76,a,b,c,d,e,f,g,76
76,77,a,b,c,d,e,f,g,77
77,78,a,b,c,d,e,f,g,78
78,79,a,b,c,d,e,f,g,79
79,80,a,b,c,d,e,f,g,80
80,81,a,b,c,d,e,f,g,81
81,82,a,b,c,d,e,f,g,82
82,83,a,b,c,d,e,f,g,83
83,84,a,b,c,d,e,f,g,84
84,85,a,b,c,d,e,f,g,85
85,86,a,b,c,d,e,f,g,86
86,87,a,b,c,d,e,f,g,87
87,88,a,b,c,d,e,f,g,88
88,89,a,b,c,d,e,f,g,89
89,90,a,b,c,d,e,f,g,90
90,91,a,b,c,d,e,f,g,91
91,92,a,b,c,d,e,f,g,92
92,93,a,b,c,d,e,f,g,93
93,94,a,b,c,d,e,f,g,94
94,95,a,b,c,d,e,f,g,95
95,96,a,b,c,d,e,f,g,96
96,97,a,b,c,d,e,f,g,97
97,98,a,b,c,d,e,f,g,98
98,99,a,b,c,d,e,f,g,99
99,100,a,b,c,d,e,f,g,100
100,101,a,b,c,d,e,f,g,101
101,102,a,b,c,d,e,f,g,102
102,103,a,b,c,d,e,f,g,103
103,104,a,b,c,d,e,f,g,104
104,105,a,b,c,d,e,f,g,105
105,106,a,b,c,d,e,f,g,106
106,107,a,b,c,d,e,f,g,107
107,108,a,b,c,d,e,f,g,108
108,109,a,b,c,d,e,f,g,109
109,110,a,b,c,d,e,f,g,110
110,111,a,b,c,d,e,f,g,111
111,112,a,b,c,d,e,f,g,112
112,113,a,b,c,d,e,f,g,113
113,114,a,b,c,d,e,f,g,114
114,115,a,b,c,d,e,f,g,115
115,116,a,b,c,d,e,f,g,116
116,117,a,b,c,d,e,f,g,117
117,118,a,b,c,d,e,f,g,118
118,119,a,b,c,d,e,f,g,119
119,120,a,b,c,d,e,f,g,120
120,121,a,b,c,d,e,f,g,121
121,122,a,b,c,d,e,f,g,122
122,123,a,b,c,d,e,f,g,123
123,124,a,b,c,d,e,f,g,124
124,125,a,b,c,d,e,f,g,125
125,126,a,b,c,d,e,f,g,126
126,127,a,b,c,d,e,f,g,127
127,128,a,b,c,d,e,f,g,128
128,129,a,b,c,d,e,f,g,129
129,130,a,b,c,d,e,f,g,130
130,131,a,b,c,d,e,f,g,131
131,132,a,b,c,d,e,f,g,132
132,133,a,b,c,d,e,f,g,133
133,134,a,b,c,d,e,f,g,134
134,135,a,b,c,d,e,f,g,135
135,136,a,b,c,d,e,f,g,136
136,137,a,b,c,d,e,f,g,137
137,138,a,b,c,d,e,f,g,138
138,139,a,b,c,d,e,f,g,139
139,140,a,b,c,d,e,f,g,140
140,141,a,b,c,d,e,f,g,141
141,142,a,b,c,d,e,f,g,142
142,143,a,b,c,d,e,f,g,143
143,144,a,b,c,d,e,f,g,144
144,145,a,b,c,d,e,f,g,145
145,146,a,b,c,d,e,f,g,146
146,147,a,b,c,d,e,f,g,147
147,148,a,b,c,d,e,f,g,148
148,149,a,b,c,d,e,f,g,149
149,150,a,b,c,d,e,f,g,150
150,151,a,b,c,d,e,f,g,151
151,152,a,b,c,d,e,f,g,152
152,153,a,b,c,d,e,f,g,153
153,154,a,b,c,d,e,f,g,154
154,155,a,b,c,d,e,f,g,155
155,156,a,b,c,d,e,f,g,156
156,157,a,b,c,d,e,f,g,157
157,158,a,b,c,d,e,f,g,158
158,159,a,b,c,d,e,f,g,159
159,160,a,b,c,d,e,f,g,160
160,161,a,b,c,d,e,f,g,161
161,162,a,b,c,d,e,f,g,162
162,163,a,b,c,d,e,f,g,163
163,164,a,b,c,d,e,f,g,164
164,165,a,b,c,d,e,f,g,165
165,166,a,b,c,d,e,f,g,166
166,167,a,b,c,d,e,f,g,167
167,168,a,b,c,d,e,f,g,168
168,169,a,b,c,d,e,f,g,169
169,170,a,b,c,d,e,f,g,170
170,171,a,b,c,d,e,f,g,171
171,172,a,b,c,d,e,f,g,172
172,173,a,b,c,d,e,f,g,173
173,174,a,b,c,d,e,f,g,174
174,175,a,b,c,d,e,f,g,175
175,176,a,b,c,d,e,f,g,176
176,177,a,b,c,d,e,f,g,177
177,178,a,b,c,d,e,f,g,178
178,179,a,b,c,d,e,f,g,179
179,180,a,b,c,d,e,f,g,180
180,181,a,b,c,d,e,f,g,181
181,182,a,b,c,d,e,f,g,182
182,183,a,b,c,d,e,f,g,183
183,184,a,b,c,d,e,f,g,184
184,185,a,b,c,d,e,f,g,185
185,186,a,b,c,d,e,f,g,186
186,187,a,b,c,d,e,f,g,187
187,188,a,b,c,d,e,f,g,188
188,189,a,b,c,d,e,f,g,189
189,190,a,b,c,d,e,f,g,190
190,191,a,b,c,d,e,f,g,191
191,192,a,b,c,d,e,f,g,192
192,193,a,b,c,d,e,f,g,193
193,194,a,b,c,d,e,f,g,194
194,195,a,b,c,d,e,f,g,195
195,196,a,b,c,d,e,f,g,196
196,197,a,b,c,d,e,f,g,197
197,198,a,b,c,d,e,f,g,198
198,199,a,b,c,d,e,f,g,199
199,200,a,b,c,d,e,f,g,200
200,201,a,b,c,d,e,f,g,201
201,202,a,b,c,d,e,f,g,202
202,203,a,b,c,d,e,f,g,203
203,204,a,b,c,d,e,f,g,204
204,205,a,b,c,d,e,f,g,205
205,206,a,b,c,d,e,f,g,206
206,207,a,b,c,d,e,f,g,207
207,208,a,b,c,d,e,f,g,208
208,209,a,b,c,d,e,f,g,209
209,210,a,b,c,d,e,f,g,210
210,211,a,b,c,d,e,f,g,211
211,212,a,b,c,d,e,f,g,212
212,213,a,b,c,d,e,f,g,213
213,214,a,b,c,d,e,f,g,214
214,215,a,b,c,d,e,f,g,215
215,216,a,b,c,d,e,f,g,216
216,217,a,b,c,d,e,f,g,217
217,218,a,b,c,d,e,f,g,218
218,219,a,b,c,d,e,f,g,219
219,220,a,b,c,d,e,f,g,220
220,221,a,b,c,d,e,f,g,221
221,222,a,b,c,d,e,f,g,222
222,223,a,b,c,d,e,f,g,223
223,224,a,b,c,d,e,f,g,224
224,225,a,b,c,d,e,f,g,225
225,226,a,b,c,d,e,f,g,226
226,227,a,b,c,d,e,f,g,227
227,228,a,b,c,d,e,f,g,228
228,229,a,b,c,d,e,f,g,229
229,230,a,b,c,d,e,f,g,230
230,231,a,b,c,d,e,f,g,231
231,232,a,b,c,d,e,f,g,232
232,233,a,b,c,d,e,f,g,233
233,234,a,b,c,d,e,f,g,234
234,235,a,b,c,d,e,f,g,235
235,236,a,b,c,d,e,f,g,236
236,237,a,b,c,d,e,f,g,237
237,238,a,b,c,d,e,f,g,238
238,239,a,b,c,d,e,f,g,239
239,240,a,b,c,d,e,f,g,240
240,241,a,b,c,d,e,f,g,241
241,242,a,b,c,d,e,f,g,242
242,243,a,b,c,d,e,f,g,243
243,244,a,b,c,d,e,f,g,244
244,245,a,b,c,d,e,f,g,245
245,246,a,b,c,d,e,f,g,246
246,247,a,b,c,d,e,f,g,247
247,248,a,b,c,d,e,f,g,248
248,249,a,b,c,d,e,f,g,249
249,250,a,b,c,d,e,f,g,250
250,251,a,b,c,d,e,f,g,251
251,252,a,b,c,d,e,f,g,252
252,253,a,b,c,d,e,f,g,253
253,254,a,b,c,d,e,f,g,254
254,255,a,b,c,d,e,f,g,255
255,0,a,b,c,d,e,f,g,0

@COLORS

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  3 109   0   0
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 15 255  36   0
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 18  73  73   0
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 20 146  73   0
 21 182  73   0
 22 219  73   0
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 24   0 109   0
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 27 109 109   0
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 30 219 109   0
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 54 219 219   0
 55 255 219   0
 56   0 255   0
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102 219 146  85
103 255 146  85
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110 219 182  85
111 255 182  85
112   0 219  85
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118 219 219  85
119 255 219  85
120   0 255  85
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123 109 255  85
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125 182 255  85
126 219 255  85
127 255 255  85
128   0   0 170
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130  73   0 170
131 109   0 170
132 146   0 170
133 182   0 170
134 219   0 170
135 255   0 170
136   0  36 170
137  36  36 170
138  73  36 170
139 109  36 170
140 146  36 170
141 182  36 170
142 219  36 170
143 255  36 170
144   0  73 170
145  36  73 170
146  73  73 170
147 109  73 170
148 146  73 170
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150 219  73 170
151 255  73 170
152   0 109 170
153  36 109 170
154  73 109 170
155 109 109 170
156 146 109 170
157 182 109 170
158 219 109 170
159 255 109 170
160   0 146 170
161  36 146 170
162  73 146 170
163 109 146 170
164 146 146 170
165 182 146 170
166 219 146 170
167 255 146 170
168   0 182 170
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170  73 182 170
171 109 182 170
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173 182 182 170
174 219 182 170
175 255 182 170
176   0 219 170
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182 219 219 170
183 255 219 170
184   0 255 170
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190 219 255 170
191 255 255 170
192   0   0 255
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194  73   0 255
195 109   0 255
196 146   0 255
197 182   0 255
198 219   0 255
199 255   0 255
200   0  36 255
201  36  36 255
202  73  36 255
203 109  36 255
204 146  36 255
205 182  36 255
206 219  36 255
207 255  36 255
208   0  73 255
209  36  73 255
210  73  73 255
211 109  73 255
212 146  73 255
213 182  73 255
214 219  73 255
215 255  73 255
216   0 109 255
217  36 109 255
218  73 109 255
219 109 109 255
220 146 109 255
221 182 109 255
222 219 109 255
223 255 109 255
224   0 146 255
225  36 146 255
226  73 146 255
227 109 146 255
228 146 146 255
229 182 146 255
230 219 146 255
231 255 146 255
232   0 182 255
233  36 182 255
234  73 182 255
235 109 182 255
236 146 182 255
237 182 182 255
238 219 182 255
239 255 182 255
240   0 219 255
241  36 219 255
242  73 219 255
243 109 219 255
244 146 219 255
245 182 219 255
246 219 219 255
247 255 219 255
248   0 255 255
249  36 255 255
250  73 255 255
251 109 255 255
252 146 255 255
253 182 255 255
254 219 255 255
255 255 255 255

Can anybody who knows Python make a demon spiral?

[wildmyron]

I really liked my far-fetched analogy to cyclic CAs

I also liked it, so here is a rule file:

Code: Select all

<rule file>

Can anybody who knows Python make a demon spiral?

Here is a naive example. To see it in action: randomly fill the universe and cut a hole about 20 x 20. Paste the pattern near the centre of the hole and run. Golly runs this pretty slowly on my laptop to begin with, so a smaller universe may be preferable. I'm not sure if it really is a good analogy to IceNine as Cyclic CA don't really have moving objects as such and the nature of Cyclic CA kind of points to the existence of this kind of object - though I agree it's extremely unlikely to occur naturally from small scale experimentation, particularly with a 1,000,000 state CA. This demon spiral doesn't seem to impose it's spatial structure on the universe, but it does cause every cell to become periodic with period 256.

Code: Select all

x = 16, y = 16, rule = Cyclic256:T1000,1000
.ApFpGqLqMrRrSsXtAuFuGvLvMwRwS$yOBpEpHqKqNrQrTsWtBuEuHvKvNwQwT$yNCpDpI
qJqOrPrUsVtCuDuIvJvOwPwU$yMDpCpJqIqPrOrVsUtDuCuJvIvPwOwV$yLEpBpKqHqQrN
rWsTtEuBuKvHvQwNwW$yKFpApLqGqRrMrXsStFuAuLvGvRwMwX$yJGXpMqFqSrLsAsRtG
tXuMvFvSwLxA$yIHWpNqEqTrKsBsQtHtWuNvEvTwKxB$yHIVpOqDqUrJsCsPtItVuOvDvU
wJxC$yGJUpPqCqVrIsDsOtJtUuPvCvVwIxD$yFKTpQqBqWrHsEsNtKtTuQvBvWwHxE$yE
LSpRqAqXrGsFsMtLtSuRvAvXwGxF$yDMRpSpXrArFsGsLtMtRuSuXwAwFxG$yCNQpTpWrB
rEsHsKtNtQuTuWwBwExH$yBOPpUpVrCrDsIsJtOtPuUuVwCwDxI$yAxXxWxVxUxTxSxRxQ
xPxOxNxMxLxKxJ!