shouldsee wrote:The idea is that if entangling is present, neighboring cells should assciates with each other by sharing mutual information.
x = 60, y = 60, rule = B4678/S35678:T60,60
13bo3b22o$9bob28o$7bob30o$5bob33o$2b38o$42o5b7o2b2obo$43o2b15o$60o$60o
$60o$60o$60o$60o$60o$60o$60o$60o$47obo2bobobob3o$45o13b2o$42obo15bo$
40o19bo$ob38o$4b33obo$6b28obo$6b24ob2o$7b2ob19o$11b17o$13bob13o$16b11o
$20b3o4$53b4o2bo$o51b8o$3o48b9o$3o46bob9o$3o44bob11o$4o43b13o$4o40b16o
$6o37b17o$6o37b17o$8o33b19o$8o4bo27b20o$15o25b20o$15ob3o18bob21o$23o
13b24o$24o11b25o$24o11b25o$23o11b26o$15ob2o2b2o11b27o$10o22b28o$obobob
ob2o17b2o2b28o$25b26ob3o$23b23ob3o$22b23o$22b23o$20b24o$20b21obo$18b
22o!
x = 60, y = 60, rule = B014/S2:T60,60
20b3o$20b4obo$19b7o$13b2o3b9o$17b12o$15b15o4bo$15b15ob3o2bo$15b17ob4o$
14b25o14b2o$14b24o$13b26obo11b2o$12b29obo8b2o$12b31o7b4o$10b34o5b3obo$
9bob41obo$8b44obo$9b43obo$2bo5b45o3bo$3o4b27ob10obo3b4o2b4o$32obo2bob
2ob3o8b8o$31o9b3o10b7o$30o11bo11b7o$29o21bob8o$28o21b11o$29o21b10o$29o
21b10o$28o22b10o$28o11b2o9b10o$29o9b3o9b10o$26obo11b4o7b10o$25o12bob3o
7b11o$25obo9bob5o8b9o$26o8bo2b5o9b9o$27o5bob7obo6b11o$28o5b9o3bo4b10o$
45obo2b11o$45o3b12o$47ob12o$45o2b13o$60o$60o$19o2b39o$7ob10o4b38o$5ob
2ob8o6b2ob34o$6o4b8o10b32o$3o6b8o12b9o2b20o$obo8b7o10b9o4b19o$11b8o11b
6o5b18o$12b7o11b5o5b18o$12b9o9bob2o6b19o$12b8o13bo6b17o$11b10o19b17o$
11b10o18b17o$12b11o18b15o$12b10o19bob13o$12b11o19b15o$12b11o21b7o4bo$
13b10o23b4o$13b3ob6o24bo$19b4o!
Bullet51 wrote:The rule B378S126 may be a good sample to test. How many states are there near Bunc=0?
Bullet51 wrote:The entropy for each cell is 1 bit. Since there is strong "entangling", the mutual information for two adjacent cells is also ≈1 bit. Such data may lead to results that the rule is somewhat complex, but in fact, it's just a voter rule.
Bullet51 wrote:There seems to be some issue on the cov statistic: Different H-I behavior may yield similar cov values.
Is there any statistics that can capture the non-linear behavior of the H-I graphs?
Bullet51 wrote:The H and I time series differ much from convectional time series, mainly from the auto-correlation profile:
x = 90, y = 90, rule = B345678/S012678:T90,90
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$
90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
o$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$44o2b44o$o
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$90o
$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$
90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
o$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobo$90o$obobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobo$90o$obobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobo$90o$obobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$90o!
wildmyron wrote:I am curious how the rule below fits into the classification scheme you have been working on here.
There are no known gliders but it seems possible that there are gliders of a sort on some periodic tiling.
25
30
32s
40s
41
45
54
57s
60
75
86
89
90
96ss
97
101
102
105
106
107
110
120
121
122s
124
126s
129s
135
136s
137
146s
147
149
150
151s
153
160s
161s
165
169
182s
183s
192ss
193
195
225
shouldsee wrote:wildmyron wrote:I am curious how the rule below fits into the classification scheme you have been working on here.
There are no known gliders but it seems possible that there are gliders of a sort on some periodic tiling.
HI wildmyron,
Unfortunately I can't remember exactly how I undertook the classification earlier on. I remember heavily relied on the notion of mutual information which I had just touched upon. The algorithm was largely based on statistical inference and I am not quite sure whether they were really valid.
I might not able to re-classify them under the earlier notation (since I was hugely disappointed by them after realised that I can be quite biased when interpreting my result). The pleasure I had was limited to the discovery of new exciting rules containing gliders, but it was more like a manual annotation rather than a machine one. Thus, I regret to tell you I might not be able to redo the classification under the earlier framework (because it was too, too messy from my current perspective).
Apologies for not being helpful.
Feng
shouldsee wrote:Bullet51 wrote:
And how on earth did you find such amazing rules?
Thank you for you appreciation. The short answer is: I don't know. The discovery of checkerlife is merely an accident: I was trying to stabilise [B12e3eijkr4ejqrtwz5cn6-ce7e/S01c2in3aejkr4ejkqtyz5ckq6-a], and attempted various modifications, and some mod give up to puffers and guns.
shouldsee wrote:PS: What's the best file format to exchange graph structure?
x = 172, y = 119, rule = B12a3en4cintwyz5aejky6-in7c8/S1e2cin3-akr4-eijkr5eijry6-a78
b2o4b2o4b2o2b4obobob2obob2ob2obobob2ob2obob2ob2ob2ob2obobob2ob4obob6ob
ob2ob2obobob2obobob2obobobobobob6obobobobobob2ob2ob6obobobobobobobobob
obobo5b2o$bo2b3o3bobo2bobo14bobo7bobo4bobobo2bobo7b3o7bo3bo4b3o6b2o20b
2o9bo3b2o2b2o5bo5bo3bo3bo3bo2bo7bo$obob3obobo2b2obobo5b3obo2bobob2obob
2obob2o2bobobobobob2o3b4o4b3obobo4bob3obo3bo2bo3b4o8b2ob4ob2o4b3o2bob
2ob6o5b3ob3ob3ob3obob3obo$2ob6ob2o5b3o3b2obob2obobo2b2obo2b3o3bobo5b3o
3bobobobob2o5bo7b3obo4b2ob2ob4ob2o4b2o6bobo2b5ob3o2bo5b4ob6o5b3o2bobob
o2b3o$2bobobob2o2bo5bo2b2ob2obobobo3bo2b4obob3obo2b2o3bob2o2bo2b2ob2o
2bo2b7o2bo4bob5o4b2o5b3o4bo2bo2b2ob3o2bobob2ob2o4bo4b6obo6bobo3bobo$2b
o2bobo2b2o2b2obob2obo2b2obobo2b2ob3ob6o2bobob2ob3o3b2o4b6obo2bobobob2o
bo2bobo2b3obob3o6bob2o2b2o2b2ob3o4b4ob2o2bo2bo2bobobobo2bo2bo3bobobobo
b4o$2bobob4o2bo2bobo3bobobobob5ob2ob4ob8ob2obobob2o4bob2obob5obobobo2b
o2bo3b2obob3ob4ob3obob3ob2obobo3bo3bo2bobobo3bob4ob5o3bobobobobo2bob2o
$bo2bo2bobo2b3o3b3obobob2ob2obo3b7o2bobobobobobo2bob2ob2ob4ob2o2bob5ob
o6b2o6b2ob2obob2obo2b4o2bobobobo3b2ob4obo2bob4obob2o2b5obobobob3o2bobo
$obobo3b3ob2obob5obob3ob3obob6o3b4o2bo2b4ob2ob6obobob3ob7ob3obobobobob
ob4obobo2b3obobo2bob3ob2o2b4obobobob3ob3o3bobob2ob3obobob5o$obob4ob2ob
2ob3obob2ob3ob3ob2ob2ob2o3b5obo3bob2ob5ob2o2b4obob9obob4obo2bobobo2bob
obo2b3obobo2bobobobobobobob3obo2bob5o2b4ob4ob5ob3o2bobo$obo2bo2bob3obo
b2o3b8o2bob8o2b5ob2o3b6obob2o2bob4ob9obobo3bobobobob6ob4obobob4obob2ob
4ob3o3b4obobob5obob2ob3obobobob2o$4ob11ob4obob2o3bob9o3bob4obo2b2o3bob
obobob3obob10obobob2o4bobob4obobobo2bob6obobo2b2o2bo2bo2b5obob9obobo2b
obobobobo3b2obo$bobob3ob9ob8ob4ob2obo2b2ob2o5b11obob3obo2b2obobo2bobob
obob2ob2o2b2obob4obob4obobob2o2b3o3bobob2obobob6obobobobob4obob3obo3b
3o$2bobo4b4o2b3obo2b3obob2obob4ob3o2b2o2bob3ob2obobob5obob2ob2ob4obobo
bob4o3b2obob8obob2ob2obob2o2bo2b4ob5o2bobobob5obobo2bobobobobob4o5bo$o
5bo2b2ob4o2bobob2obobo2bob3ob2obobob2o2bobobob3obobob5obo4bo3bobobobob
obobobo3bobobo4bobo2bobobobo2b2obobobob2obob10obobobob4obobo2bobobob4o
bo$4o3b4obob2ob3ob2o3bobo2bobob2ob3obo3bo2b4o3bobobobobobobobobob2obob
obobob5o2bo2b3ob2obobo2bob7ob5o2b5o2b3obobob5obob2obobobob3o2b5o2bo2bo
$o2b2obobob2obo2bob10ob2obob2ob3obob3obobobobobobob5obobobo4bobob3ob7o
bob2ob2obob2obo2bo2b2obobobobobob4obob14obob2obobobob4obo2bobo2bo$o5b
2ob4ob4obobobo2bobo4b3o2b3obobobob5ob3obobobobo3bobobo2bobobo3bobo2b2o
2bobobo3bob5o2b10obobobob2o3bobobo2bob3o3bobob5obobo3bo3bobo2bo$2bo2b
3ob5o2b3ob4ob3ob9obob3obobob5o3b8ob2obob4obob3obobob3o2b3ob3o2b2o4b4ob
o2bob3ob2obob3o2bob8ob2o2bob2ob2ob2obob3o2bo$obobob3o2b4o3bo2b2ob3obo
2bob2ob2ob5o2bob7obobobo2bobobo2b3obob4obob4obo3bob4ob3ob4obob2o4b3obo
bo3bobo2bobobobo2bob5o2bobobo5bo2b2o7bo$4b4ob3ob2ob16o3bobobobobobob2o
b3o2bob3ob6obo2b3o3bo2bobo3b5ob9o2b5obo2b6obobob2o2b13obobobo2bob2obo
2b3ob7o$obob2ob2ob2o6b10ob3o2bob9o2b3obob6obo2bobobob2o2b2obob4ob2o2b
2ob3ob13ob2ob3obo2bobobo4b3obobobob4obo2bobobob5obob2ob3o3b2obo$2b6o4b
6ob9ob2ob4obobobobo2bobo3bo3b2ob3o2bobob2o2b2o3b2ob4obobobo2b13obob2ob
3ob3obobob15obob8obo3bobob4o2b2o2bo$o3b3ob21obob2o2bob6obob2obobo3b2ob
3o5bob5obob3o3b6obob14o2b8o2bobobo2b3obob3obo2b4obob3obob7obobobo3bobo
bo$2o3bob3ob4ob11ob2ob3obobobobobo2bobo2bo2b2o2bob4obo2b2obob2ob4ob2ob
ob4ob11ob2ob8obob3obo2b17ob3ob13ob4obo$b2o2bob3ob7ob7o2bobobobobob7o2b
ob3o3b3o2bo3b4obob6ob2ob2o5bobobob10o2bo2b4ob7o2bobobob7obobobobob4o2b
7obo2bob2obobobo$4obob2obob3ob9ob3ob2obobob2ob2obobob2obob2o2bob3o2bo
4bob3ob9ob3o2bob10o2bob2ob11obobob6ob8ob2o3bobobob8ob6o2bo$obobo2bob2o
b13ob3ob3obobobo2b4obobo2bob8obob5ob5ob4obobo2bo2bob2ob8o4b2obo2bob6ob
obobob11ob3ob18o3bo3b2obo$2b7obobobob11o2bobobobob2o2b2o2bo2b2obo2b5ob
2ob5ob7o2b2o2b2o2b3obob11o2b4o2b8obobobobobob8o5bobobob3obobobob3o3b2o
$o2b2ob6obo2b11obobobobob6obobob3obob3obo3b2ob4o2bobob2o2b3o2bobo2bob
2o2b9ob2ob3o2bob2o2b2obobobobobob7obobob4obobob8o4b2obo3bo$3bobob2ob3o
bo3b10o3bobo2bob3obo3bobobo2bob2obo2bobobobo3bob3o2b2obob2obobobob18ob
2ob7obob3obob8obo2b2ob3o2b4obobo2bobob3ob2o$5ob4o4bob2ob10obobo2bob3ob
o3b3obo4bobobo3b5o2b2obob3obo2bobo2b4ob10o2b8ob2o3bobob5obobob16o4b7ob
obobobobobo$b3obobob2ob2obo2b10ob4obobobobob2o2bobobob2obobo2b2obobo6b
ob2ob3ob2obobobo3bob7ob14ob2obob5obobob4ob3obob4o2b2o2bob4o2b6o4bo$b2o
bob3o2bobob3ob9ob3obobobobo2bobob4obobo2b4ob7obobo2b2ob2o2bob3o3b4o2b
4o3b9ob4o2bobob2obobobobob6obobo3bobo3bob12ob2o$2obob3ob8ob2o2bo2b8obo
bobob7obobobo2bobobobobob4ob5obo3bobo3b3o2b7ob3ob6obobo2bob5obob2obobo
bobob7o3b2obobobob6ob3o2bo3bo$3bo3bobobobobob2ob5ob5ob4obobo2bobob4obo
b10obob6o2b2o2bo2b3o4bo3b3obobobob8ob2ob2ob4o4bobob3ob2obob3ob6o2bobob
6obob4obo$o2b4obob10obobo2bob4obo2b3o4bo2b3obob4obobobobob9ob3ob2o2b6o
2b10o3b6o5bob8obobob3o2b5ob6obo2bob8obo2b4o2bo$3b2o2bobobobobob9o2b3ob
3ob4ob2ob2ob2obo2bobob8obob3o3b3o3b8o2b3obobobobob5o2b2ob16ob2o3bobobo
3b4obobo2bo2b2o2bobobo4bo$o4b2obob6obobobobob3ob4ob7ob2ob2ob3o3bobob2o
b3obob2ob2o2b2o2b2ob2ob2o2b2ob2ob12ob2ob5obob5obobob2o3bob3o2bob2o2bob
obo2b3ob2obob2o2b2o3bo$2b3ob2obobob2o2b15ob4obob7obobo2bobobob6o2b3obo
5bobob4obob2obo2b3obobobob2ob4ob7ob8ob2o2bob2o2bob5ob4obo6bob2obobobo$
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4obob3obobobo2b3o2bo5bob2o2bobob2o2b2ob4o2bobo2bo2bo$ob3o2bobobob2o2b
2ob2ob4o3bo2b4ob10ob2o2bobobobob2obo2bobob3ob13ob6obo5b3o2b6o2b3obob9o
b2ob2obo3b11ob5obobobob2ob2o$b3ob3o2b5o2bo2bobobobobo2bobob2o3bob6ob3o
b2obobobo2bob3ob2ob13ob3ob5obobobo5b2ob4o3b3obobobobo2b2ob3o3b9obob2ob
obo2b2o2bo2b3ob3o$ob5o2bobobobob3obo3bob2o3b2ob3ob2ob5o3bob2ob3obob6ob
o3b13o2bo2b4obobobobobob3obob3o2bobob5o2bo2b2ob7ob14o2bo3bo5b3o$obobo
3bobob4obob2ob3obobo2bobo2b3o3b6ob3ob7obobo3bo2bobo2b9obo3bob6ob2o2bob
10obob3o2bobobob11obob7ob2ob2o6bob2o2bo3bo$2bob2obob3obobob2o2b3obo4b
3o3bo4b4obobob3ob13obob3o2b9obo3b11o3bobob2o2b2obobobob3o2bobo2b5o2b2o
bo2bob14o2b5ob3o$obob3ob4ob6o2b2obo2b2ob3obob9ob4o3b9o2bobo3b3obob10ob
obob7obobob6o2b9ob6obo2b5ob5o2b2ob2obob2obo3b3obo5b3o$2bob6obo3bobobob
5o2bo2b6ob4ob7o2bob4ob2obob5obo2bo2b16ob4obobob2obobo2b3obobobob2obobo
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obobobobob3o!
shouldsee wrote:...we can at least figure out some incremental changes along a mutation path. More specifically, the Hamming distance between 2 given rulestrings is distorted. Starting from B3/S23, B23/S23 changes the dynamics greatly with 1 bit flipped, whereas B368/S238 endures 3 flipped bits but bears great similarity to B3/S23. Thus it'd be great if we can find a universal way to quantify the dynamical difference between 2 given rules given their rulestring, or at least spot the important bits of a given rulestring. (obviously not all 102bits in a nt-rule is important)
BlinkerSpawn wrote:There's no real way to do this purely theoretically, because - as I'm sure you realized - the Hamming distance treats all bits equally when we know they should not be. (e.g. B0 definitely changes dynamics much more than S8)
However, in my mild experimentation with non-totalistic rules there is one thing I have noticed, that being cognizant of the relative frequency of certain neighborhoods gives one greater control over dynamics, which leads to my little rookie's suggestion:
BlinkerSpawn wrote:Instead of expressing dynamic difference purely on the difference between rulestrings, weight the changed neighborhoods based on the frequency in which they appear naturally in the two rules. (I say check both rules to preserve transitiveness of the dynamic difference and give a more refined estimate)
This may be difficult for rules with large differences in dynamics that cause very disparate "transition profiles", but it looks like it could still be a better approach that a naive Hamming comparison.
shouldsee wrote:BlinkerSpawn wrote:Instead of expressing dynamic difference purely on the difference between rulestrings, weight the changed neighborhoods based on the frequency in which they appear naturally in the two rules...
Just to clarify, I am not "expressing dynamic difference" with difference between rulestrings, I used correlation to do that. I simulate say 500 soups on a 20x20 torus for 11 steps, and collapse all trajectories into 500x20x20x11 bits, and check the correlation between the 2 sets of trajectories (one from each rulestring). The hamming distance is merely there to restrict searching depth to nearby rules (so that we only calculate similarity between superficially/naively related rules! )
I hope this clarifies a bit.
Thus it'd be great if we can find a universal way to quantify the dynamical difference between 2 given rules given their rulestring, or at least spot the important bits of a given rulestring.
BlinkerSpawn wrote:I still think it would be a better determinant of what constitutes a "superficially related rule", considering that even though specific profiles (what I think you call trajectories) can vary between rules, certain transitions are basically always more or less important than others (e.g. 2a or 2e as opposed to 2n). So you could say that a bitflip in 3a or somesuch may or may not constitute a "superficial variation" and better fine-tune your search.
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