Use Smoothiness to classify rules

For discussion of other cellular automata.
shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Use Smoothiness to classify rules

Post by shouldsee » July 30th, 2016, 11:06 am

Links:Lifespan on a torus another photo

UPDATE: The method used to classify rules is being continually updating. Many entropy-related statistics have been tried out to describe the behaviour of a rule.

It's been noticed that a neighborhood transition map based on input-configuration(neighborhood,NH) of the cell rather than input state (0 or 1) is useful in revealing the dynamics of the space. Furthermore, forward entropy and backward entropy can be measured for individual NH, ascribing a point to each NH in a 2 dimensional entropy space, where a transition is represented by a directed vector starting and ending on these points.

The asymmetry between forward entropy and backward entropy is noticed in entropy space for complex rules, and it's been suggested this discrepancy reflects vectorial/directional propagation of localisation in the universe. Later it was shown some extreme asymmetry actually comes from strobing effects common in B0/S8 rules, irrelevant to the complexity of the dynamics itself. To correct this effect, NH is taken between snapshots separated by 6 steps (thus correcting for both p2 and p3).

To further quantify this asymmetry between FE and BE, flux is measured on the aforementioned 2-D entropy space, along FE+BE axis and FE-BE axis. Transition vectors are projected onto axes and the absolute length of their projection summed for each axis, weighted by the propensity of corresponding transition. Complex rules is expected to show a strong flux along the FE-BE axis for frequent transitions between forward-uncertain NH and backward-uncertain NH. The result came out, in contrary, to support the opposite.

Random soups are tested for each rule and their mf(FE-BE),mf(FE+BE),m(input entropy) are measured to ascribe a 3-D point. Complex rules are actually associated with a large mean flux along FE+BE axis (large mf(FE+BE)), forming a piece of boundary of the rulespace. A cluster of chaotic/random rules is located in mf(FE+BE)=1~1.5, mf(FE-BE)=0.6~0.8, mean(input entropy)=3~4. It is worth noting, that another cluster lies near the origin viewed in 2d, which in 3d scattered along the m(input entropy) axis. These rules have relatively small mf(FE+BE) and mf(FE-BE) thus are not effectively classified by this method.

In addition, synchronisation of replicator stream is also noticed to show interesting dynamics, in both B0123458/S02356 and in B02345/S034


Archive:
Hi mates,

It has long been desirable to quantitatively describe the complexity of a cellular automata. Building on the 'input entropy' idea [1], the concept of smoothness emerges from the time-evolution of entropy.

Here I define smoothness as the frequency spectrum (fourier transform) of the autocorrelation profile(ACP) of the input entropy. The idea is that change in entropy can be decomposed into different frequencies, with the lowest frequency corresponding to smooth behaviour, and period 2 behaviour corresponding to frequency of 0.5. etc.

EDIT: Actually the Fourier transfrom of ACT has its own name: Spectral power distribution (SPT)

EDIT: Later I found the aforementioned way isn't consistent/robust enough. Instead I now apply a entorpy-recurrence-based method to measure the smoothness of the rule.

The general idea is
1. acquire input entropy
2. construct return map by convolution with FIR1 and then thresholding (absolute value >0.001)
3. calculate return rate (this is a fairly standard statistics for return map).
4. combined with max-min entropy, mean population to identify interesting rules.

FIR1=
1 -1
-1 1


I have undertaken a scan of the v2k9 B/S rulespace (it's actually an subspace of v2k8 outer-totalistic rulespace) to obtain some preliminary results on a 30*30 torus for 102 effective steps/

maxamplist='max amplitude'
mmlist=' (max - min)entropy'

EDIT:
Below is a clip of statistics
AVG stdev's
1entropy 2entropy 3entropy 4entropy
0.2833 0.0569 0.4352 0.0643 0.1077 0.0439 0.1576 0.0599 B012/S025
0.0544 0.0623 0.0766 0.0551 0.1889 0.2247 0.2383 0.1528 B01347/S0134
0.0478 0.0586 0.0642 0.0445 0.1006 0.1712 0.1643 0.1450 B0123457/S0346
0.0233 0.0000 0.0125 0.0010 0.0000 0.0000 0.0000 0.0000 B0124567/S12345
0.0233 0.0000 0.0125 0.0010 0.0000 0.0000 0.0000 0.0000 B0124567/S12345
0.0011 0.0012 0.0013 0.0024 0.0036 0.0028 0.0023 0.0056 B36/S0124567


Please do post any rules you want smoothness to be tested so that we build a comprehensive spectrum.

The next question, naturally , is then how comes that some rules transmits at specific frequencies and other rules have a distributed frequency.

Kind regards
Feng Geng

Reference:
[1]Wuensche, A., 2011. The DDLab Manual (Preview) 2nd ed.,p478,s.33.1

PS: The current version of matlab script can be found here. (updated 08/22/2016 @ 9:32am (UTC))
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Last edited by shouldsee on October 20th, 2016, 12:59 pm, edited 12 times in total.

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Re: Use Smoothiness to classify rules

Post by shouldsee » July 30th, 2016, 3:51 pm

Come back to check Often! Will occasiaonally update!.

Some interesting patterns from my search of rulespace

Ordered emergence, reflected as periodicity on time/space/both:
Including oscillators, spaceships, agar crawlers, gun


Rules with gliders/moving heads as strong attractors (meaning they are really abuandant)

Sierpinski growth

Code: Select all

x = 16, y = 14, rule = B0137/S12
12b2o4$10bo4bo$2bo3bo$o7bo$o7bo$2bo3bo$10bo4bo4$12b2o!

Code: Select all

## In this pattern the replicator synchronised onto one direction. This might have allowed parallel streams to store more information.
## At 85000 generations a vectical replicator stream attacked a horizontal repliactor stream to turns it into vertical.

x = 62, y = 62, rule = B0123458/S02356:T512,512

bo4bo2bo4b5o4b2ob2ob4obobo4b3ob6o2bob2o$6b2ob2obo2bo3b3obo2bo4bo7bo4b
2o8b3o3b2o$bo2bo7bob5obo2b2ob2ob3ob2o2b13o3bob3o3bo$bo2bo2bob2o2b2o2b
4ob4ob3ob3obo3bo4b2o3bob3o2bo3b2o$4b3obo2bobob2obo9b2ob3ob3o2bobo3bo2b
4obo3bo$4b2ob2ob3ob2obob4o4b4o2bob2o2b2ob2ob2o2bo2bo2b2o2b3o$bobo5b2ob
ob3ob3o5b2ob3o2bobob2o2b2o5bobobobob2o2bo$4b3o3bob2ob5obo3b2ob4o5bo2b
2o4bo6bobobob2o$2bo2b2o2bobo2bob2o2b3ob3o4bobob3obobo4bo3b3ob2o3bo$b3o
b2o2b4obob3o2b2obob2ob3o4b4o3bob3ob2obo2b2obo2bo$bo2bobobob8obobobo2b
2obo2bobo2bob2o5bo2bobobo2bo2bobo$3bob3ob2o4b2ob2ob2o4bob2o2b3o6bo3b2o
b2obo2b4obo$2b3obob2o2bobo2bo4b2obo2bo2bo2bobob2ob4o2bo2bobo2bobo2bo$
3bob2o2b2obobobobob2o2bo2b4o2bo4bo2bo2b2obo2bo3b3obo$b2o3b2o2bob2obob
2ob5o2b3o5b4ob3obobo2bob3o2b2obobo$b2o4b2o3b6ob2ob4o5b2o3bo2b7obo3bo2b
2o2bo$2bobo6bo2b2o3bo5b4ob4o3b3o2bobo3b2ob4o3b2obo$3bo8bo3b3o2b2obobob
obo2b2ob3ob2o2bob3ob4o2b2ob3o$bob2obob3ob4o4bobo5b3o3b2o2b2o2b4ob4o5b
2o2b2o$3b4obobobobo5bo2b3ob4o3b4o3bob3ob3o4bo2b2o2bo$2bo4b3obob2o2bobo
2bob2o2b5ob9o3bobobo2b3o2b2obo$bobo4bo3b2obo3b2o2bob4obob5ob2obo2bob2o
b4o4bo2bo$b4o3b3obo4b7o4bob3obob3obobo2bo2bo2bo4bob3o$2bo3b2o3bob2ob2o
4b2o3b2obo2bo2b2ob2o5bo3bob2ob2o2b3o$bo2bob3o2b2o3b2o2b7o5bob2o4b3o2bo
3b2o2bo3bobobo$bobobobobo3bo2bobo2bo2bob2obob2o4bob2o7b3obo3bobob2o$3b
2o2bo3b2ob2o2bo2b2o2b9obo2b3ob5ob2ob2o2bobo$bob2obo2bo4b2ob3o2b5o3bo5b
obobob5o3b2ob6o2bo$bob3o3b6o3b3ob2obo4b6o2b3o4b4o3bob4ob2o$bo3b3ob4o2b
o4bobobo2bo2bo4b5o2bobo2bob3obobob3obo$bobob3ob4o3b4o2b2o2b3o2bo4b3o2b
obo5bobo3bob2o2bo$2b3ob6o2bob2ob4o2b2o2bo2b2o4bo2bo2bobo4b3obob2o2bo$b
4ob2obo2b2ob3obob2o2b2o2bob2o2bob2o3b2obo2b3ob3obo2bobo$2bo2b3obobo2bo
2b3o2b2o3bobobo8b3ob2obo3b2ob3obobo$2b3o4bob4o5b3o2b3obo3b3obobobob2o
3b3obo4bobo$bo3bob2ob6o2bo2bobo4bobo4bob2obob11ob6obo$2bo2bob2o2b7ob2o
4bo2bob2obob3obobob2ob2ob2o4bo2b2o$bob2o3b2o4bobo2b2ob2ob3obo2b2obo3bo
b2o2b2o3b2o4b3obo$bobobob4o2b2ob4obo4bob6ob4obobobo2b4o2b3o5bo$bobo5bo
bo3bob4o3bob2o5b2o2bo3b5ob2ob2ob2o4bobo$2bo7b4o5bo2bobob3obo2bo4bob4ob
ob7o4bo$3bobob2obob3obob2o2b2obo2bo2b2obobobo9b2o2bobo3bo$b5o3bobobobo
bo2b2ob6o3b2o2b2ob2ob2obobobo6bo3bo$bob2obob2o2bob2o3b2ob2o2bob5o4bo2b
6o2b3o3b3ob2obo$bob4ob2o2b5ob2o3b3o4b2obo4bo4bob7ob2o3b4o$b2ob2o3bo4b
2o4b2o3b3o2b5o2b2ob3ob2obobobo3bo3b2o$bob2ob3o6bo5bobob2ob4obo3bo3b3o
2bob2o4b2o3b3o$3b2o2b3ob2obo3b2ob2obobobo5bo2bo2bo3bo2b3ob2obo3b2o$bo
2bob3o3bobob3o2b2obob4o3bobo5bo3bo2b2o2b2obo3bobo$2b2o3b2obobo3b4obob
5obobo2bo2bob2o2bo4bo2b2o2bo2bob2o$bob3ob4obobo4b4obo2b5ob2o4b2obob2o
2bobo3b2obo3bo$4b9ob2o2bob2obobo2bobo2b3obob4o2bobo2bobo2bobobobo$2bob
3o2b3obobobob2o5b3o4bo2bo2bo3b7ob2obob2ob3o$b3o3bo3b2ob3o2b5o3bo3bo2b
2o2bobob2ob2obo2b2obo3bo$6bo2bobob8o3b3o3bobob4obo2bo2bo2b2ob3o2bobo2b
o$b7o3bo9b2obo3bob2ob2ob2o5b5o2b4ob4ob2o$bob2o4b2o2bob2obobob2ob2obob
3obob2o2bobo5bob6o$3b2o3b2obo5b2obo2b4obo5b2obob5o2b4obo3b2ob2obo$bo2b
3ob4ob4o3bob2o4bobo5b2o4b2o2b2o5bo2b2o3bo$3b5obob2ob3o2b2o2b2obob2ob2o
4bo5bo2bobo4b2o6bo$3bo5bo2b2o3bobobobo3b4o2bob2obobobobobob4ob2obobo2b
o$bobob2obob6o3b3ob2o2b4o3bo2bobo5bo5bo2b2o4b2o!
Birdy (Maybe better be called 'Bat')

Code: Select all

x = 4, y = 4, rule = B014/S2
2b2o$b3o$obo$bo!

Code: Select all

x = 107, y = 89, rule = B01234/S0146:S512
4$101b2o$101b2o$101b2o7$48b2o$48b2o$48b2o3$48b2o$40b2o$39b4o$40b2o6b2o
$39b4o5b2o$40b2o6b2o6$48b2o$40b2o6b2o$48b2o2$47bo54b2o$39bo2bo5bo52b4o
$38b6o4b3o51b2o$37b2ob2obo2bo2bo51b4o$36b2ob6o3bo53b2o$35b2ob8o3bo$34b
2ob8o$30bo4b13o$30bo4b13o3bo$34b2ob8obo$35b2ob6ob2o$36b2ob4ob2o$37b2ob
2ob2o$38b6o$39bo2bo2$102b2o$101b4o$102b2o$101b4o$102b2o11$40b2o$39b4o
59b2o$40b2o59b4o$39b4o59b2o$101b4o$102b2o$39b4o$40b2o$39b4o$40b2o2$40b
2o$39bo2bo$38bo4bo$38bo4bo$38b2o2b2o$38bo4bo$40b2o60b2o$40b2o59b4o$
102b2o$39bo2bo58b4o$40b2o60b2o3$104b3o!

Code: Select all

x = 24, y = 50, rule = B015/S03:T128,128
2$18bo$10bob6o$10bo7bo4$18bo$3bob13o$3bo14bo8$6bobo$6bo11$13bo3bo$8bob
o2bo3bo$8bobo2bo3bo$13bo3bo10$11bo5bo$9bo3bobo3bo$9bo3bobo3bo$11bo5bo!

Code: Select all

x = 53, y = 66, rule = B01378/S123:T128,128
11$15bo$12bo2b2o3bo7bo7bo7bo7bo$12bo11bo7bo7bo7bo$14bo12$19bo$9bo$7b2o
b2o4bo4bo2bobob2o3bob2ob2ob2ob2ob2obo$7b2ob2o4bo4bo2bobob2o3bob2ob2ob
2ob2ob2obo$9bo$19bo7$10bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$6bo$4bo$4bo2$
8bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo9$12bo$7bobo$7bobo4bo2bo!

Code: Select all

x = 50, y = 50, rule = B02345/S0234:T128,128
o$o$o!

Code: Select all

x = 57, y = 74, rule = B0178/S12:T128,128
5$3bobo$3bobo14$41bo$36bo$13bo13bobo13bo$4bobo14bo3bo2bo2bo9bo3bo$4bob
o14bo3bo2bo2bo9bo3bo$13bo13bobo13bo$36bo$41bo16$26bo7bo11bo$13bo4bo6bo
9bo$5bo14bobo2bo2bobobo2bo2bo$5bo14bobo2bo2bobobo2bo2bo$13bo4bo6bo9bo$
26bo7bo11bo12$31bo15bo$6bo7bo$4bo3bo16bo11bobobo$4bo3bo16bo11bobobo$6b
o7bo$31bo15bo!

Code: Select all

x = 45, y = 40, rule = B014/S12
9$6b21o$4bo22bo$3b25o$3b25o$4bo23bo$6b22o7$6b2o$6b2o$7b2o6$8b2o$8b3o$
6b5o$6b3o$7b2o!

Code: Select all

x = 34, y = 29, rule = B0136/S123
4$7b2o$6b4o2$4bobo2bobo$3b2o2b2o2b2o$3b2o2b2o2b2o$4bobo2bobo2$6b4o$7b
2o8$23b2o2$23b2o2$23b2o!

Code: Select all

x = 95, y = 120, rule = B01346/S023
8$35bobobo$36b3o$36b3o$35bobobo11$33b2o$35bo$35bo$30bo3bo$31b3o16$33bo
$34bo$34bo$33bo20$41bo14bo14bo8bo$28b14ob14ob14ob9o$28b54o$80bo36$13b
2o$12bo2bo!

Code: Select all

x = 139, y = 81, rule = B0124/S025
32$40bo$37b2o3b5o$37bob6o2bo$37b3ob7o30b2o2b2o2b2o2b2o3bo$37b12obo11bo
9b2o2b19ob2o$29b2o5b13o8b4o10b26obo$28b6ob15o3bo2bob6obo2bo2b27obo$29b
2ob17o3bobob6o2b2obob30obo$29bob21o2bo2b5o3b20o2b14o$30b13ob8o2b9obob
18ob2ob13o$27b15o2b5o2bo4b3o3b16obob2obo3b4o3b4obo$30b12obobobobobo3b
2o2b2o3b12o8b3o3b8obo$28b10obo3b2o10bobo8b2ob7o22bo$30b7ob2o4bo16bo4bo
bo17bo5b3o$29bo2b2o28b2o3bo2b5o$62bo!

Code: Select all

x = 75, y = 207, rule = B01245/S235
28$34b3o$33bo3b2o$33b7o$33b8o$33b9o$33b9o$33b8o$33b7o$33bo3b2o$34b3o
38$28bo$28bob4ob3o$28b3o4b5ob3o$28b13o3b2o$28b3o3b13o$28b20o$28b21o$
28b21o$28b20o$28b19o$28b3o5b5o3b2o$28bob3ob6ob3o$28bo6bobo$35b2o39$37b
o$35bobob4ob3o$32b2o2b4o4b5ob3o$31bo2b16o3b2o$31b9o3b13o$30b27o$29bob
27o$29bob27o$29bob26o$29bob25o$30b10o5b5o3b2o$33b5ob3ob6ob3o$32b6o6bob
o$33b2o9b2o$33bo27$39b3o$39b5ob3o$38b7o3b2o$38b13o$38b14o$38b15o$38b
15o$38b14o$38b13o$40b5o3b2o$38b6ob3o$39bobo$39b2o!

Code: Select all

x = 31, y = 97, rule = B01234/S012357:T100,100
6$11bob4obo$10b2o6b2o$10bob6obo$10b2o6b2o$11bob4obo13$3b3o$3bo2bo14bob
4obo$4bo2b2o14b4o$3bob2obo12b8o$4bo2b2o14b4o$3bo2bo14bob4obo$3b3o10$
12b3o$14b2o$12bo2bo$14b2o$12b3o10$14b3o$12bo$14b3o$10bob6obo$12b6obo$
9bob7obo$9bob6o$9bob6obo$12b3o$16bo$12b3o7$11bob2obo$13b2o$11b6o$13b2o
$11bob2obo10$12bo2bo$11b6o$12b4o$12b4o$11b6o$12bo2bo!

Code: Select all

x = 3, y = 4, rule = B01234578/S1346
b2o$o$o$b2o!

Code: Select all

x = 1, y = 2, rule = B0123456/S0346
o$o!

Code: Select all

x = 88, y = 24, rule = B013478/S013
7$6b2o$33bo48b2o$5bo2bo23bobo$82b2o$4b2o2b2o$79bobo2bobo$4b2o2b2o23bo
25b4o$38bo2bo16b6o16b2o2b2o$5bo2bo25b2o23b4o$39b2o17b6o$6b2o51b4o$58b
6o$59b4o!

Code: Select all

x = 69, y = 86, rule = B0123458/S12356:T512,512
6$28b14o$27bo$26b15obo$10b16ob16o$9bo16b17o$7b36o$6b37o$6b37o$7b36o$9b
o16b17o$10b16ob16o$26b15obo$27bo$28b14o10$18b30o$9bo7bo30bo2bo$15b35o$
14b36o$14b36o$15b33obo$17bo29bo$18b29o14$16b31o$15bo31bo$13b35obo$12b
38obo$12b38obo$13b35obo$15bo31bo$16b31o10$29b25o$28bo23bobo$26b29o$25b
29o$25b29o$26b26o$28bo23bo$29b23o$$2$5b2o$4b2o$3b3o$3b4o$4b2o!

Code: Select all

x = 300, y = 300, rule = B014/S12:T1024,1024
o2bo2bob2ob3o2b2o2bobob3o2bobobobo2bobo2bob2obob2obob2o$b4obo4b3o6b7ob
o2b2o8b2obo2b2o3bobo2b2o$o2bo4b2ob2o2bobobobo2b2o5bob2o2bobo3b3o2b3ob
2ob2o$4b3obo2b4ob5o4b4o3bobo2b2o3bo2bo5bob2o$6o3b5o2bobobo2b6o2bob2obo
b3o2b3o6bo2b2obo$bobo2bo2bo2bo2b4ob8obob2o2bob2ob3o2bo5bobo2bo$b3ob3o
4b2o2b2o3b2o2b2obo2b6o4bob2ob2ob6o2bo$bo3b2o2bob2obo2b3o2b3o2b2ob3o3bo
b2o3b2o2bob2o2b3obo$b2o2bo2b2o4bob7ob2o5b3obobob2obo2b3obobob3ob2o$obo
bo3bo2bob2ob2ob2ob2ob3ob3ob2o2b3o2b3ob4ob2o3b3o$bo4bo3bo2b2obob3o3bobo
2bobob3obo4bo2b4ob2o2b5o$3o2bob2ob2obobobob4ob6ob2obob2o2bob7ob3o$3o4b
3o3bo4bob5ob3ob3o2b2ob6o4bo5b2o2bo$o2bobob2o5bo7b2o2bobo2bo2b5obob2ob
2o2bobo3bob2o$b2obob2obobo4b5o2b3o2bo5bo3b2o2b2ob2obobo2bo2bo$obobob5o
bobo2b3obob4ob2ob2ob3o3b2o2b2o4bobo2b2obo$b3o2b6obobo4bo5bo2b2o2bobo2b
o2bo2b3ob2o3b3ob2o$bo4b4obobo5bob2o3bo2b3ob2ob2o4b3o3b2o4b4o$o2bobo2bo
b2o2bo6b4o7bo3b2obo2b2ob4ob3o2bo$2obob2o3b2o2b5obo2b2ob4o2bobo2b2o4b5o
bo3b2ob3o$2o4bo2b2o5bo3bo2b2o3b2o2b3o3bo3b4o4bo4b2o$3b2ob2obo3bo2bo2bo
2b3o2bob2o3b2o3b3ob2o2bob2o4bo2bo$4o2b2o2b3o4bob2o2bo3b2o2bob2ob7o7b2o
4bobo$b3obobo2b5obo3b2obo2b3o2b4o5b2ob2o3b2o2bobo$8bo3b3o3b2obo7bo2bo
2b2ob3ob2obobobob2o5bo$2b2ob2ob4o2b4obo2bo5b2o5b3o2bo3bob2ob3o2b2o2bo$
ob2obobo4bo4bob2o2bob9o5b5o4bobob3ob3o$3ob2ob3obobobob3ob2obob2ob7ob2o
b2obobo4b2ob2o$2bo4bobo6bobo2bo2b4ob2o3bo2b2obobo3bo4b3o3bo$bo3bo2b3o
2b3o2b3o3bo4b2ob5ob4obobo3bob2obob3o$obo3bo2bo2b2o5b2ob3ob4o5bo2b6o4b
6o3b2o$obobob2o4b3o3b2o6b3o4b2ob2obo2bobob2ob2o3b2o2bo$obo3bobob4obo2b
obo2bo4bo3b2ob2ob2o2b3o2bo2b2ob2o3bo$4ob2o2b2ob3ob2obobobo2bob2obo2bob
3o2bo3b3o5b3o2bo$3o3b2ob2obobob2o4b3o3b4o4b2o3bo3b3o2b2obobobo$bobo2bo
2bo2bobobo2bobo2b2o4b3ob5o3bob3o2b8obo$2bob4o3bo4b4ob2o5b2ob3obo3b3ob
4obo2bobobobo$4b2o2b5obobo3bob4ob4obob2obo2bob3o3b2ob3o2b3o$4ob5o3b3o
2b2obo3bob2obo7b3ob3ob2ob2obo3bobo$bo2b2obo2bo3b2o3b2obo2b3o4bobo4b2ob
2o4b3o4b2o$2o2bo2bo2b3o4bob2o2b2ob5obo3b3o2bobob2o3bo5b3o$b4o2b4ob2ob
2obob2o2bob2o4bo3b2ob2ob3obob6ob2obo$2b2o4b8obob5ob3o2b2obo2bo3bob2ob
13o$2bobo2b4obo5bo2b2obo2bo2b4ob2o4b2o3b5ob3o2bo$2ob4obobo3b2o6b3obob
5o2bob5obo4b4obo2bobo$bo4bob2obo2b3o2bo2b2o5b5ob4o2b2o2b4obo3bob2o$o2b
o2bo3b2ob5o2b3obob2obo3bo4bo3b2obob3ob4ob2o$3o6bo7bob2o3bo3bob5o3bob2o
5bobob2obo$bob2o2bobob2obo2b2obo2bo2bob2o3bo2b4obobo2bo3bobob3obo$ob2o
2bo2b4o4bo2bo3bobo6bo2bobo4bob2ob3obo2b3o$4b3o3bob4obobobobo6b2o2b4obo
2b2ob5o2b2obo2bo$o5bo3bob4o2b2obo2b2o2bobobob7o2b2obobo4b3o2bo$2b2o2b
2ob2ob5ob3ob2o4bobo3b5o2bob3ob3o2bo2bob2o$ob2obo2bo3b2o3bob2ob3obo3bo
2b2ob2o2b3obo2bob2o2b4obo$2o2b3obo2bo2b2ob3obob9o2b3o6bo7b2obob2o$obob
ob3ob3o2bobo3b2o5bob4obo3b4ob4o2bo3b2o2bo$bob2obo4bo3b3obo2bo4bo5bobo
2b4obob4o3b3obobo$obob5o2bobob2obobo2bob3o2b5o3b3obob2obo5b6o$2o2bobo
4bo2bo5b2obobo3b7o3bobob3o3b3o2bo2bo$b3ob3obob3ob3ob3ob3o2b3o4b2o2bob
2ob2ob6o2bo$6b3obob4obob4o2b3o4bo3b3o3b7ob3ob2ob2o$o2b2o3bobob2obo4b2o
bob2o2b2o5b2obo2bobo3b8ob2oo2bo2b3ob2o3b3ob2o$bo4b4obobo5bob2o3bo2b3ob2ob2o4b3o3b2o4b4o$o2bobo2bo
b2o2bo6b4o7bo3b2obo2b2ob4ob3o2bo$2obob2o3b2o2b5obo2b2ob4o2bobo2b2o4b5o
bo3b2ob3o$2o4bo2b2o5bo3bo2b2o3b2o2b3o3bo3b4o4bo4b2o$3b2ob2obo3bo2bo2bo
2b3o2bob2o3b2o3b3ob2o2bob2o4bo2bo$4o2b2o2b3o4bob2o2bo3b2o2bob2ob7o7b2o
4bobo$b3obobo2b5obo3b2obo2b3o2b4o5b2ob2o3b2o2bobo$8bo3b3o3b2obo7bo2bo
2b2ob3ob2obobobob2o5bo$2b2ob2ob4o2b4obo2bo5b2o5b3o2bo3bob2ob3o2b2o2bo$
ob2obobo4bo4bob2o2bob9o5b5o4bobob3ob3o$3ob2ob3obobobob3ob2obob2ob7ob2o
b2obobo4b2ob2o$2bo4bobo6bobo2bo2b4ob2o3bo2b2obobo3bo4b3o3bo$bo3bo2b3o
2b3o2b3o3bo4b2ob5ob4obobo3bob2obob3o$obo3bo2bo2b2o5b2ob3ob4o5bo2b6o4b
6o3b2o$obobob2o4b3o3b2o6b3o4b2ob2obo2bobob2ob2o3b2o2bo$obo3bobob4obo2b
obo2bo4bo3b2ob2ob2o2b3o2bo2b2ob2o3bo$4ob2o2b2ob3ob2obobobo2bob2obo2bob
3o2bo3b3o5b3o2bo$3o3b2ob2obobob2o4b3o3b4o4b2o3bo3b3o2b2obobobo$bobo2bo
2bo2bobobo2bobo2b2o4b3ob5o3bob3o2b8obo$2bob4o3bo4b4ob2o5b2ob3obo3b3ob
4obo2bobobobo$4b2o2b5obobo3bob4ob4obob2obo2bob3o3b2ob3o2b3o$4ob5o3b3o
2b2obo3bob2obo7b3ob3ob2ob2obo3bobo$bo2b2obo2bo3b2o3b2obo2b3o4bobo4b2ob
2o4b3o4b2o$2o2bo2bo2b3o4bob2o2b2ob5obo3b3o2bobob2o3bo5b3o$b4o2b4ob2ob
2obob2o2bob2o4bo3b2ob2ob3obob6ob2obo$2b2o4b8obob5ob3o2b2obo2bo3bob2ob
13o$2bobo2b4obo5bo2b2obo2bo2b4ob2o4b2o3b5ob3o2bo$2ob4obobo3b2o6b3obob
5o2bob5obo4b4obo2bobo$bo4bob2obo2b3o2bo2b2o5b5ob4o2b2o2b4obo3bob2o$o2b
o2bo3b2ob5o2b3obob2obo3bo4bo3b2obob3ob4ob2o$3o6bo7bob2o3bo3bob5o3bob2o
5bobob2obo$bob2o2bobob2obo2b2obo2bo2bob2o3bo2b4obobo2bo3bobob3obo$ob2o
2bo2b4o4bo2bo3bobo6bo2bobo4bob2ob3obo2b3o$4b3o3bob4obobobobo6b2o2b4obo
2b2ob5o2b2obo2bo$o5bo3bob4o2b2obo2b2o2bobobob7o2b2obobo4b3o2bo$2b2o2b
2ob2ob5ob3ob2o4bobo3b5o2bob3ob3o2bo2bob2o$ob2obo2bo3b2o3bob2ob3obo3bo
2b2ob2o2b3obo2bob2o2b4obo$2o2b3obo2bo2b2ob3obob9o2b3o6bo7b2obob2o$obob
ob3ob3o2bobo3b2o5bob4obo3b4ob4o2bo3b2o2bo$bob2obo4bo3b3obo2bo4bo5bobo
2b4obob4o3b3obobo$obob5o2bobob2obobo2bob3o2b5o3b3obob2obo5b6o$2o2bobo
4bo2bo5b2obobo3b7o3bobob3o3b3o2bo2bo$b3ob3obob3ob3ob3ob3o2b3o4b2o2bob
2ob2ob6o2bo$6b3obob4obob4o2b3o4bo3b3o3b7ob3ob2ob2o$o2b2o3bobob2obo4b2o
bob2o2b2o5b2obo2bobo3b8ob2oo2bo2b3ob2o3b3ob2o$bo4b4obobo5bob2o3bo2b3ob2ob2o4b3o3b2o4b4o$o2bobo2bo
b2o2bo6b4o7bo3b2obo2b2ob4ob3o2bo$2obob2o3b2o2b5obo2b2ob4o2bobo2b2o4b5o
bo3b2ob3o$2o4bo2b2o5bo3bo2b2o3b2o2b3o3bo3b4o4bo4b2o$3b2ob2obo3bo2bo2bo
2b3o2bob2o3b2o3b3ob2o2bob2o4bo2bo$4o2b2o2b3o4bob2o2bo3b2o2bob2ob7o7b2o
4bobo$b3obobo2b5obo3b2obo2b3o2b4o5b2ob2o3b2o2bobo$8bo3b3o3b2obo7bo2bo
2b2ob3ob2obobobob2o5bo$2b2ob2ob4o2b4obo2bo5b2o5b3o2bo3bob2ob3o2b2o2bo$
ob2obobo4bo4bob2o2bob9o5b5o4bobob3ob3o$3ob2ob3obobobob3ob2obob2ob7ob2o
b2obobo4b2ob2o$2bo4bobo6bobo2bo2b4ob2o3bo2b2obobo3bo4b3o3bo$bo3bo2b3o
2b3o2b3o3bo4b2ob5ob4obobo3bob2obob3o$obo3bo2bo2b2o5b2ob3ob4o5bo2b6o4b
6o3b2o$obobob2o4b3o3b2o6b3o4b2ob2obo2bobob2ob2o3b2o2bo$obo3bobob4obo2b
obo2bo4bo3b2ob2ob2o2b3o2bo2b2ob2o3bo$4ob2o2b2ob3ob2obobobo2bob2obo2bob
3o2bo3b3o5b3o2bo$3o3b2ob2obobob2o4b3o3b4o4b2o3bo3b3o2b2obobobo$bobo2bo
2bo2bobobo2bobo2b2o4b3ob5o3bob3o2b8obo$2bob4o3bo4b4ob2o5b2ob3obo3b3ob
4obo2bobobobo$4b2o2b5obobo3bob4ob4obob2obo2bob3o3b2ob3o2b3o$4ob5o3b3o
2b2obo3bob2obo7b3ob3ob2ob2obo3bobo$bo2b2obo2bo3b2o3b2obo2b3o4bobo4b2ob
2o4b3o4b2o$2o2bo2bo2b3o4bob2o2b2ob5obo3b3o2bobob2o3bo5b3o$b4o2b4ob2ob
2obob2o2bob2o4bo3b2ob2ob3obob6ob2obo$2b2o4b8obob5ob3o2b2obo2bo3bob2ob
13o$2bobo2b4obo5bo2b2obo2bo2b4ob2o4b2o3b5ob3o2bo$2ob4obobo3b2o6b3obob
5o2bob5obo4b4obo2bobo$bo4bob2obo2b3o2bo2b2o5b5ob4o2b2o2b4obo3bob2o$o2b
o2bo3b2ob5o2b3obob2obo3bo4bo3b2obob3ob4ob2o$3o6bo7bob2o3bo3bob5o3bob2o
5bobob2obo$bob2o2bobob2obo2b2obo2bo2bob2o3bo2b4obobo2bo3bobob3obo$ob2o
2bo2b4o4bo2bo3bobo6bo2bobo4bob2ob3obo2b3o$4b3o3bob4obobobobo6b2o2b4obo
2b2ob5o2b2obo2bo$o5bo3bob4o2b2obo2b2o2bobobob7o2b2obobo4b3o2bo$2b2o2b
2ob2ob5ob3ob2o4bobo3b5o2bob3ob3o2bo2bob2o$ob2obo2bo3b2o3bob2ob3obo3bo
2b2ob2o2b3obo2bob2o2b4obo$2o2b3obo2bo2b2ob3obob9o2b3o6bo7b2obob2o$obob
ob3ob3o2bobo3b2o5bob4obo3b4ob4o2bo3b2o2bo$bob2obo4bo3b3obo2bo4bo5bobo
2b4obob4o3b3obobo$obob5o2bobob2obobo2bob3o2b5o3b3obob2obo5b6o$2o2bobo
4bo2bo5b2obobo3b7o3bobob3o3b3o2bo2bo$b3ob3obob3ob3ob3ob3o2b3o4b2o2bob
2ob2ob6o2bo$6b3obob4obob4o2b3o4bo3b3o3b7ob3ob2ob2o$o2b2o3bobob2obo4b2o
bob2o2b2o5b2obo2bobo3b8ob2o!

Code: Select all

x = 7, y = 5, rule = B0137/S14
$2bobo$2bobo!
Last edited by shouldsee on August 23rd, 2016, 12:32 pm, edited 47 times in total.

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Re: Use Smoothiness to classify rules

Post by shouldsee » July 31st, 2016, 1:18 pm

Emergent complex/hierarchial behaviors:

Code: Select all

x = 35, y = 35, rule = B01237/S2345
bo3b4o3b7o2bo6b7o$ob2o4bo2b6o2b2o5b2ob2o$3b4obobo3b3o2bobobo3b2o2b2o$o
2b3o3b4obob2obo2bob3obo3bobo$bob2obob6ob2o2bob4o3b3ob2o$bo2b2obob2o2b
3o2bo3bo3bo3bo2bo$2o3b2o2bobob2obobo5bob4o3bo$4o3b4obobo3bo7bobobo3bo$
3obo4b2o2b5ob5obo3bob4o$3ob3ob4o3bo2b4o4bo5b2o$o2bo2bo5b5ob2o4bo3bo2bo
bo$b2ob3ob2o2bo3bo2bob4ob5obo$2b3obobo2bo2bo2b4o4bobobo2bo$obobobo2b2o
bo2b2obo2b4ob3ob3o$b2o2bob2o3b4obo2bo2b2obo4bo$2ob3o5bo2bob3o3bo2b3o2b
ob2o$ob3o3b2o2bo5bobobo4b3o$b2obob2ob2ob3o2bo2bo2b3o3b2o$obobobo5b2o4b
obo2b3obobo2b3o$o3bo3bobob2ob3ob7ob4o2b2o$o3b2obo4b2ob5ob2o3bob2ob3o$
2o4bobobo4bobo2bobo3bobo2bobo$2o2bob2o6b3o2bo2bob2obobo2bo$8b3o2b2o4b
3o3b2ob3o2b2o$2ob4obobo2bobo2b2obo2bobo3bo$2bo3b2obobo2b2ob2o3b4ob2ob
2o$obo3bobob2o4b6o2b5o2b4o$o4b2o4bobobob3ob4o3bo2b2obo$2bo2b5o2bobo5b
2o2bobob2o3bo$2b2o2bo4bob2ob2o3b5o2bobo3bo$4obo2bo2b5ob2ob5o3bobo$2bo
2b4o5b2ob4o4bobobobo2bo$3bobobobo3b4o4bob2obo2b2o2b2o$o4bo4b2obob5o2bo
bo2bo2bo2bo$b2o5b2o5bob8o3b7o!

Code: Select all

x = 97, y = 86, rule = B0568/S8:T100
3o2b10o2b14ob21ob3o3b7o3b21o2b4o$9b6o2b2o2b2ob5ob9ob2ob11ob7ob4o7b8ob
8o3b3o$9b6o2b2o2b17ob3ob11ob2obob6o4b8ob2o2b11ob2o$3o2b10o2b12ob12o2b
7ob2ob3ob10ob10ob2ob13o$3o2b10o2b9ob15o4b2ob8ob11ob13o2b2ob9o$3o2b2o2b
2o10b18ob3o3b5ob17ob3o4b6o2b8ob3o$3o2b2o2b2o10b4ob4o2b3ob15ob4o3b2ob6o
b3ob3o3b3o3b7o$3o2b10o2b13ob5ob3ob20ob17o7b7o$3o2b10o2b6ob24ob2ob12ob
17o4b7ob3o$9b6o2b12ob16o2b9o4b4ob3ob5ob6o5b2ob3ob3o$9b6o6b8ob3ob3ob2ob
13o7b4ob4ob3ob3ob3ob3ob5o2b3o$3o2b10o4b6ob3ob6ob6ob11o7b11ob4o2b13o3bo
$3o2b10o4b7ob28o4b19ob10ob3o3bo$3o2b2o2b2o8b11ob24o4b9o2b7ob5ob9o$3o2b
2o2b2o5b3o2b14ob18ob3ob3o2b4ob3ob3ob5ob3ob5o$3o2b10ob3o6b20ob29ob5o2b
3ob2ob2o$3o2b10ob6ob44ob7ob17ob3o$9b7o3b10ob25ob5ob9ob3ob3ob17o$9b7o3b
14ob10ob3ob3o13b3o3b14ob3ob7o$3o2b8ob2ob3o2b6o3b19ob3o4b3ob3ob3ob16o2b
9o$3o2b8ob2ob3ob23ob9o4b11ob16o2b9o$3o2b2o2b4ob2ob3ob20ob3ob8o2b2ob10o
b3ob3ob8o2b9o$3o2b2o2b4ob4o3b15ob3ob7ob3o4b4o2b2o11b14o2b3ob2o$3o2b8ob
6o4b15ob8ob2ob2o2b8o4b3ob17o5b3o$3o2b8ob6o2b22ob3ob5o2b2ob2ob5ob3ob8o
4b5o2b6o$9b11ob25o3b2ob2o4b4ob11ob22o$9b10ob10ob5ob2ob6o3b8ob4ob12ob
19obo$3o2b10o5b4ob2obob6ob9o3b8ob11ob4ob10ob5ob4o$3o2b10o5b3o2b2ob7ob
12ob12ob10ob16o3b3obo$3o2b2o2b2o9b3o2b2ob7ob6ob5ob6ob4o2b27o3b5o$3o2b
2o2b2o9b4ob2obobob3ob3ob5ob10ob2ob9ob2ob9o2b5o4b2o$3o2b10o2b7ob2ob2ob
3ob29ob3ob4o4b12o4b2o$3o2b10o2b14ob2ob10ob10o3b14ob3ob3ob4o7b2o$9b6o2b
6ob10ob3ob3ob3ob6ob2o3bob28o4b4o$9b6o2b10o2b2ob3o7b4ob6ob7ob2ob2ob3o2b
16o4b3o$3o2b10o2b10o2b2ob3ob3o2b9ob6ob4obob7ob3ob3ob3o2b3o7bo$3o2b10o
2b10o2b2o2b2ob3o2b4ob12ob5ob10o2b3ob5ob3o5b2o$3o2b2o2b2o9b3ob3o2b2o2b
2ob3o2b3ob4ob4ob3ob3o4b2ob6o2b3ob5ob3o2b5o$3o2b2o2b2o9b7o2b2o2b2o2b3ob
7ob4ob8o4bob2o2b3o6b5ob3o2b5o$3o2b10o2b7o5b14ob15ob2o4b6o9b6o5b5o$3o2b
10o2b7o5b15ob7ob7obo5b6o8b6o8b2o$9b6o2b2o2b2o10b10ob3ob3ob4ob8ob9o2b3o
b6o8b2o$9b6o2b2o2b2o10b8ob8o2b3ob3obobob5ob5o2b3ob6o8b2o$3o2b10o2b10o
2b14ob7ob3ob3ob2ob5o4b3o2b4ob15o$3o2b10o2b10o2b14ob2ob5o4b11ob8ob20o$
3o2b2o2b2o10b6o2b2o2b22o2b6ob12o2b2o2bob3obobobo2bo$3o2b2o2b2o10b6o2b
2o2b4ob2ob14ob3ob3o2b5ob7obo2b8ob2o2b2o$3o2b10o2b10o2b26ob4ob19o8bobob
o3bo$3o2b10o2b10o2b8ob14o4b4ob9ob6o6b10o3bo$9b6o2b2o2b2o10b20o4b3ob16o
6bobob5o4bo$9b6o2b2o2b2o10b10ob3o2b4ob5o2b3o3b5ob4o6b2ob2obob6o$3o2b
10o2b10o2b10o2b12ob6o3b7ob4obob7ob3ob2obob2o$3o2b10o2b10o2b10o2b12ob2o
b3o3b16ob5ob3ob6o$3o2b2o2b2o10b6o2b2o2b2o6b3o3b3ob3obob3o3b14ob5o3b3ob
7o$3o2b2o2b2o10b6o2b2o2b2o6b3ob11ob2o4b6ob3o4b6o8b5o$3o2b10o2b10o2b10o
2b2ob11o2b2o4b6ob4o3b8o3b3o2b4o$3o2b10o2b10o2b10o2b12ob5o4b3o4b4o8b9o
2b4o$9b6o2b2o2b2o10b6o2b2o2b10ob3o11b7ob3ob9o2b4o$9b6o2b2o2b2o10b6o2b
2o2b2ob5ob2o14b7ob11o7bo$3o2b10o2b10o2b10o2b14ob3o9b12ob8o4b4o$3o2b10o
2b10o2b10o2b12ob5o9b3o2b16o4b4o$3o2b2o2b2o10b6o2b2o2b2o10b6o2b2o2b5o3b
6o2b6o3bob5o4b4o$3o2b2o2b2o10b6o2b2o2b2o10b6o2b2o2b5o3b6o2b4ob9o3b3ob
3o$3o2b10o2b10o2b10o2b10o2b11ob6o4b4ob14o2bo$3o2b10o2b10o2b10o2b10o2b
18o4b19ob2o$9b6o2b2o2b2o10b6o2b2o2b2o10b17ob3ob5o3b3ob6o$9b6o2b2o2b2o
10b6o2b2o2b2o10b17ob4ob4ob4o2b6o$3o2b10o2b10o2b10o2b10o2b10o4b3ob3ob4o
6b4o2b6o$3o2b10o2b10o2b10o2b10o2b10o4b4o5b3o6b4o2b6o$3o2b2o2b2o10b6o2b
2o2b2o10b6o2b2o2b2o8b8o7b3o7b5o$3o2b2o2b2o10b6o2b2o2b2o10b6o2b2o2b2o9b
7o7b3o7b5o$3o2b10o2b10o2b10o2b11ob10ob11o7b5o3b3ob3o$3o2b10o2b10o2b10o
2b11ob10ob6o12b5o3b7o$9b6o2b2o2b2o10b6o2b6o2b3o5b6ob2o2b3o11b5o3b7o$9b
6o2b2o2b2o10b6o8b4ob4ob5ob3o2b4o18b6o$3o2b10o2b10o2b14ob12ob9o3b3o18b
3obobo$3o2b10o2b10o2b14ob12ob9o4b2o14b6ob4o$3o2b2o2b2o10b6o2b2ob3ob7ob
3ob6o3b6ob2o4b2o14b10o$3o2b2o2b2o10b6o2b3ob7o4b3ob3o6b3o3b5o2b2o14b7o
3bo$3o2b10o2b10o2b14ob3ob3o6b3ob5obo2b2o6b3o5b3ob3o3bo$3o2b10o2b10o2b
17ob2o5b14o2b3o5b3o4b3ob3ob2obo$9b6o2b2o2b2o9b3ob14o4b14o2b7ob3ob6ob8o
$9b6o2b2o2b2o9b4ob3o3b2o2b3o4b3o2b9o3b8o2b7ob3ob4o$3o2b10o2b10o2b3ob3o
b3o2b3o3bob8ob3ob11ob5ob6o2b8o$3o2b10o2b10o2b3ob3ob29ob2obob3ob4ob3o2b
3ob3ob3o$3o2b2o2b2o10b6o2b3o7b6ob24ob5ob3o6b6ob4o!

Code: Select all

x = 50, y = 43, rule = B01234567/S02348:T50,50
12bobob4o2b6o2b6o4b4obo$12bobob3o3b3o2b4o5b3ob4o2bo$12bob5o2b7o8bobobo
2bo2bo2bo$12bo2bo2b3o2b2ob8o2bobobo2bo2bobo$12bo21b11obo2bo$12bo3bo3bo
7bo7b2o7bo3bo$12bo15bo20bo$12bo4b2o13b2o8b2o5bo$12bo3bo2bob2o2b2o2b2o
4b2ob3o8bo$12bo4b2o14bo4bob2o6bo$12bo11bo2b2o8b2ob2o2bo3bo$12bo3bo3bo
5b3o9b3o8bo$12bo11b2o7b3o$12bo2bo2b6ob3o5bobobo7b2o$12bob5o9bo3bo2bobo
2b2ob2o$12bobob3o2b4o3b2o2bo2bo4b3obo$12bobob3ob2o2b2o3b4o2b2o3b3obo2b
2o$12bobob3obo4bo10b2o2b5o2b3o$12bobob3obo4b8o4b5o2b4o$12bob5ob2ob4obo
3b3o6bo3bo$12bo2bo2b3o3bo3bo6b5obo3b5o$12bo14b3o2bo6b8o$12bo2bo5b3o3b
2o5bo5bo4bo$12bob3o3bo3bo3bo11b6o$12bo2bo5b5o4b2o3bo3b5o2bo$12bo11b3o
2bo2b5o2b5ob3o$12bo3bo7bo2bobo2bobobo3b3o2b2o$12bo12b2o2bo2bobobo$12bo
4b2o11b2o2b2o2bo7bo$12bo3bo2bo18bo7bo$12bo3bo2bo6bo$12bo4b2o11b5o2bo8b
o$12bo17b5o2bo2bo4b5o$12bo3bo5bo3bo6b2o13b2o$12bo7bobobobobo7b2o$12bo
2bo14b3o$12bob5obo4b2o3bob3o11bo$12bo2bo9b2o3bo2b2o6b3o2bo$12bo18b2o6b
6o$12bo3bo2bo3bobobo8bo2b2o2b6o$12bo3bo2bo3bo3bobo4bo3b2o4bo3b2o$12bo
25b2o4bob4o$12bo2bo18b2ob10o!

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x = 94, y = 72, rule = B12378/S18
47bobobo9bo2b30o$47bobobo9b2obob5obobobobobobobobobobobo$47bobobo10b5o
2b25o$47bobobo4bo6bobo3bobob2ob2obob2ob2obob2ob2o$47bobobo3b11o2b26o$
47bobobo3b4o3b2o2b3obobobobobobobobobobobobo$47bobobo4bo2b4o2b29o$47bo
bobo9b5obob2ob2ob7obobobobobobo$47bobobo9bo2b13o2b15o$47bobobo9b2obob
5obob2obob2obobobobobobo$47bobobo10b14o3b15o$47bobobo4bo6bo3bo2b10o3bo
bob5obo$47bobobo3b9o3bo3b2o3b3o4b11o$47bobobo3b11obo3b2o5b7obob4obo$
47bobobo4bo2bobo3b9o11b3o4bo$47bobobo8bo5b2o2b3o$47bobobo5bo2b3o5b2o
11bobo5bobo$47bobobo9b3o21bo7bo$47bobobo4bo8bobob3obobo3bobobo3bobobo$
47bobobo3b3o3bo15bo7bo7bo$47bobobo3b2o5bo5bo6bo$47bobobo3b2o4b5o4b3o8b
3o3b5o$47bobobo3b3o2b2o3b6o2b21o$47bobob2ob2ob4o4bob7ob3obobob5obob3o$
47bobob11o3b3ob2o2b3obob5obob5obo$47bobobobobobobobo3bob2o5b8ob5ob5o$
47bob13o3b4o2bo3b2o4bo4b4ob2o$47bo2bo2b14o14b6ob6o$47bo23b2o18b3o$47bo
23b2o2bo7b2o$47bo2bo2b8o5b2o9b3o$47bob13obobo2b4o3b3ob2obo2b4o$47bobob
obobobobob5o6bobo2b3obobob9o$47bobob4ob3ob2obob5o2b3o2bob3ob3obobo3bo$
47bobo3bobob2o2bobo5b4obo2b8o5b3o$47bobob4ob3o2b3o5b2ob5ob3o$47bobobob
ob7obo2b2ob4o3b3o2bobo3bo3bo$47bob6o4b2o9bo14bo3bo3bo$47bo2bo7bo8bo5bo
bo3bobobo3bo3bo$47bo29bo7bo3bo3bo$47bo3bobobobobobobobobobobobobo3bobo
5bo$47bo20bo8bo4b3o$47bo5bo5b2o2b2o3b2o2b3o6b2ob2o3b2ob2o$47bo11b2obob
2obob3ob3o3b15o$47bo3bobo9b2ob8ob7ob7ob2o$47bo8b2o7b6ob3ob3ob3ob3ob6o$
47bo2bo2b4ob8ob7obob5obob5obobo$47bob45o$47bobobobobobobobobobobobobob
ob3obobob3obobob3o$47bobob25ob7ob7obo$47bobob30ob6ob5o$47bobobobobobob
obobobobobobobobobobo4b2ob3ob3o$47bob26obobo3bo3b2ob3obo$47bo2bo2b4ob
7ob6obobobobo2bo2bob3ob3o$47bo8b2o6b3o4b10o3b4ob5o$47bo3bobobo13bo5b2o
b8ob4o$47bo11bo3bo3bo3bo4b3ob5o3bo3bo$47bo4b2o11bo3bo3bo$47bo3bo2bob2o
9bo3bo3bo3bo3bobo5bobo$47bo4b2o11bo3bo11bo4bo$47bo11bo3bo3bo4b3ob3o6b
4o$47bo3bobobo14b3ob3ob8ob7o$47bo8b2o6b15o2b3ob3ob4o$47bo2bo2b4ob7o2b
3ob2obob6ob3ob3ob3o$47bob19ob3o9b3ob4o2b2o$47bobobobobobobobobobob4o
10b6ob3ob2o$47bobob8ob8o2bo4bo2bo2b2ob2ob6o$47bobo4b4obobo8b2o5b10obo$
47bobo3b2o3b14ob2ob13o$47bobo3bo5b3ob2ob2obob3obobob2ob2obob3o$47bobo
3bo2bo4b8ob2ob2ob9ob2ob5o$47bobo3bob4o2b2obo2bobob6obobobo2bob3obobo!

Code: Select all

x = 31, y = 26, rule = B0123456/S2347
3obo2bobob2o2b2o2bobo2bo2bo$2b4obobobo3b5obob3o2b2o$4o2bobobo4bo8bobob
3o$3bobobobo3bobo8bobobobo$2ob7obo4bob2obobo3bob2o$obo3b3obobo4bobob2o
bobobobo$bo2bob4obob3obobo4b2obo$ob2o3bob2ob3ob6ob4o2bo$o2bob2o4bo2b3o
b4ob2o2bob2o$o2bobobo5bobo4b2o6b3o$o5bo5bo2b3o2b4ob2ob2o$3ob5o2b2o2b3o
3b3o2b4o$2b2ob2o7b2obo3bo3b2o3bo$bo3bo2b2ob2obob3o2b3obob3o$2ob3o4b6o
2bo2bo4b4o$bo4bo2b2ob2obob5o5b4o$3obob2o5b2ob2ob2o3b2o4bo$2obo5b2o2bob
2o2bobo2bo2b2obo$bobob5o5bo6bobo3bo$obobob3o6bo3bo2bob2ob2obo$2bobo2b
3o5b3ob2o2b2ob2o2bo$ob3o2bo4bob7o2bobo$4o4b5ob2obobo2b9o$ob4o4bobob2ob
o2bo3b4o$b4ob2o4bob2o2bob2o3b2ob3o$obo4bob6o2b2obo3bobo!

Code: Select all

#emergent higher order interaction
x = 46, y = 54, rule = B0178/S08:T60,60
6o3b3o3b4o2b4o2b4o6b7o$2b4o2b5o2b4o2b5o2b4o5b7o$2b3o3b18o3b4o2b4o2b4o$
5o4b17o3b4o2b4o2b4o$7o5b5o2b3o2b9o2b4o2b4o$3ob5o15b15o3b2o$10o3b2o6b9o
2b4ob2o$b9o2b6o2b9o3b8o5bo$b3o2b4o2b6o2b6o5b10o3b2o$4o2b4o2b6o3b4o6b3o
3b4o2b3o$4ob4o4b4o8b9o3b4o2b3o$4ob4o3b2o2b2o2b21o3b2o$4o2b2o3b20ob9o3b
2o$4o7b22ob6o3b3o$b2o4b11o2b4o6b6o7b3o$2b2o2b9o3b2o5b2o5b4o4b6o$b4ob9o
2b4o3b4o4b13o$b4o2b2o2b4o2b4o3b5o3b10ob2o$b4ob2o3b4o3b5o2b21o$b14ob2o
2b4ob14o2b5o$b3ob7ob6ob13ob5o2b4o$4o2b13ob3ob8o4b4ob4o$6o5b8ob3o2b3o2b
4o2b4ob4o$7o4b4o2b7o2b2ob5o2b8o$8o3b4o2b7o2b19o$2o2b9o4b3o2b11ob12o$2o
2b9o5b10ob4ob6o3b3o$8ob4o3bob10o2b2o2b3ob8o$2b4o4b5obo5b6o2b2o7b7o$2b
4o2b6o11b8o3b10o$2b4ob7o6b2o3b9o2b10o$3b2o2b4o2b3o3b4o3b8o2b10o$8b2o3b
4o2b4ob2o4b5o4b7o$o3b4o5b4o2b3o2b3o3b8o2b4obo$2ob16o5b3ob10o2b6o$14ob
4o2b4o2b7ob3ob7o$3ob15ob5o2b7o5b4ob2o$2o2b3o3b3ob8ob3ob3o5b11o$2o2b3o
2b2o3b4ob2o3b2ob3o4b6o2b4o$18ob2o3b6o4b7o3b2o$18ob2o3b4ob3o2b7o4bo$18o
b9o2b2o2b3o$10o2b3ob2ob8o3b2o2b3o6b2o$3o4b3o2b3o2b10o6b4o5b4o$3o4b4ob
3ob4o2b6o2b6o6b4o$6ob4ob3ob12ob7o6b4o$11o5b12ob9o4b4o$2b5ob3o5b2ob8o2b
9o4b4o$4b3ob3o5b2ob3o2b4o2b3o2b3o5b3o$o3b3ob10o2b2o2b4ob9o5b3o$2ob3o2b
14o2b4ob9o5b3o$2ob3o2b14o2b4ob10o5b2o$o2b13o2b3o3b4o6b5o6bo$2b9o7b3o3b
3o2b3o2b5o!

Code: Select all

#emergent
x = 3, y = 3, rule = B06/S8:T60,60
$b2o$bo!

Code: Select all

#emergent
x = 33, y = 35, rule = B08/S8 :T60,60
8b25o$o9b5o9b9o$o11b7ob8o2b3o$o11b7ob8o2b3o$o4b3o4b7ob8o2b3o$8o4b4o8b
4o2b3o$8o4b4o12b5o$5ob10o7b4ob5o$5ob10o7b4ob2o$6b10o7b9o$6b10o7b9o$8o
6b8ob2o2b2ob2o$8o6b8ob10o$8o6b2o4b2ob10o$8o6b2o4b2ob4o2b4o$4ob3o6b2o4b
2ob4o2b4o$4ob3o6b2o4b5o4b4o$4ob3o6b2o4b5o4b4o$4ob3o6b2o7b4ob4o$4ob3o6b
4o5b4ob4o$4ob3o6b4o3b6ob4o$12o4b11ob4o$ob13ob7o5b4o$ob6o2b5o3b3o7b4o$o
b6o5b2o3b14o$ob2o2b2o5b2o3b14o$ob6o3b9ob11o$ob6o3b9ob11o$o10b2o2b5o2b
4o$10b10o2b10o$10b7o2b14o$10b2ob4o2b14o$10b2ob4o2b4ob2o6bo$10b13ob9o$
2b21ob9o!

Code: Select all

#emergent
x = 44, y = 51, rule = B01/S56: T60,60
5b2o14b4o7b2o8b2o$5bo15bob4o4b2o5bo2b2o$10bo10b7o10b4o$10b2o6bo3b6o10b
4o$2b3o3bo2bo2b3o3bo2b5o14bo$2b5o2bobo9bob4o3b5o2b3o2bo$9bobo2bo3bo2bo
b4o3b5o7bo$7b2o2bo3b2o2b3ob13obobo3bo$3obobo5bo7bo2b2o2b4o3b2ob2obo2bo
$2obo2bobo3bo10b2o7bo2bob2obo$2obo2bo17bo4b2o2bobob2ob2o$3bo3b3o7b2o2b
2o4bo5bobo4b4o$bobo6bobo5b4o4bo6bobo4b3o$bo10bo2bo4b2o3b6o3bo$3obo4bob
2o2bo4b2o2b3o6b3o$4obo3bob2o4b5o8bo3bobo$4obo4bo3b6o2b2o6b3obo2bo$3obo
3b4o2b5o2bobo6bo2bo3bob3o$2obo3bo3b2ob4obo12bo3bob4o$2o2bo2bobo4b3ob2o
2bo7b5obob4o$2o3bobob2o2b3obo4bo2bob2ob2o3b2ob4o$b3o2b3ob5o7bo4b2o3b2o
bo2b4o$b2o4b2ob3o3bo4bo4b5o3b2o4b2o$2o9bo2b2o3bo3b9o8b2o$o6bo10bo2b5o
2b2o9b2o$2o4b2ob2obobo2bob6o8bo4b2o2b2o$2o2b3o3bobobo2bobo2b3o4bobo9bo
$o3b3o3bobo2b3o5b2o3bo11bo2bo$9b2obo5b2obob2o4bo4bo5bobo$12b5obo2bobo
10bo5b2o$b3o7b7ob2o4b2o2b2o3bo4bobo$6o3b10o3bobo2bob2o3b2o4b2o$5o4b2ob
7o5bobo2b2o3b2o5bo$4o10b4o6b2o9bo$4o3b2o3bo3b2o9bo$b3o7bo2bo2bo3b3o2b
4o$2b2o7bo3bobo5b11o8b2o$2b3o3b3obo2bobo2b2o2b10o$2b3o3b2o2bo2bob2ob2o
2b10o6b2o$3bo7bo5b3o10b5o6bo$10b2o2bo2b3o11b6obobo$11bo2bob3o14b4o2bo$
2bo8bo2bo9b6o5b2o$2bo8bo3b3o7b5obo3b5o$3o2bo5bo5bo8b2o2b3o2b7o$12b5o
18b7obo$8b3o26b5obo$10bo12bo9b3ob5o$3o15b2o3bo2b3o2b2o4b6o$6bo3bo2b2o
3b3o4bo4bo5b4ob3o$5b2o2bobo2bo3b4o2bo6bo3b9o!

Code: Select all

#emergent
x = 54, y = 60, rule = B0678/S56:T60,60
3b2o2b4o26b4o4bobobobo$3b2ob5o7bo9bo4bo3b4o2b3o$3b2o9b11o12b4o2bo$10b
2o2b3o3b5o12b2o14bo$9bo2bob3o3b6o11b2o2b2o4bo2b4o$3b2o4bo2bob3o3b6o8b
5o2b2o3bobob4o$3b2o4bo2bo4b3o3b3o10b3o6bo2bo4bo$3b2o5b2o11bo12b8obo3bo
3bo$3b5o15bo12b8obo4bo2bo$7b3o10b4o19bo2b2o2bob2o$7bo11b5o4bo10b2o2bo
4bobob2o$20b5o13bo4b4obobo2bo$4bo15b6o6bo6b2o2b4obo4bo$20bo27bo2bobo$
17b3o29b2o$3o3b2o6b2ob3o$3o4bo10b2o23b8ob2o$3obo2bo10b3o4bo6b2o6bo2b3o
6b2o$3obo2bo5b2o3b4o10b2o5bobob3o$3obo2bo10b4o3bo6b2o5b2o2b3o$b2obo8b
3o2b5o2bo2bo2bo4bo6b10o$4bobo2bo6bobo3bo5bo2bo2bob3o6b8o$o3bobob2obo2b
2o2bo3b8o2b2o2b3o6b8o$2o3b2o2bobobo4bo3b2o5bo6b3o3b2o2b2o3b3o$2obobobo
3bobo4b6o2bo5b9o2b2o2bo$2o4b3o3bo5bo3b2o2bo8b7o2bo2bo2b2o$obo4bobo29b
3o5bobo3bo$o2bobob2o2b5o10bo5b2o5b3o3b2o2bo$o2bobo4b3o7bo11b2o5b8o$o2b
o6b3o3b2o2bo18b8obo$o3bo2b6o3b2o3bo21b4obo$b3obob6o3b3o2bo21b2o3bob4o$
7b6o3b4o7bo2bo9b2ob2o2bobo$7b14o6bo2bo15bo2bob3o$3b25o5b2o5bo6bobo$3b
9o3b9o5bo3b2o13bob2o$5bo9b8o3bo2bo19bo2bo$2o3bo3b2o4b8o4bobo2bo17bo$2b
o5bo2bo4b3o3bo4bobo2bo5bo11bo2bo$2bo5bo3b2o2b3o3bo2bobobo5b4o6bo4bo$2b
o5bob5o2b2o3b2o2b2o6b5o7bo2b2o$2bo4bobo4bo2b2o3b3o6bo2b5o11bo$o2b4o2bo
b2ob2ob2o3b3o6bo6bo11bob2o$bo7bo4b2o2bo4b6o6bo2b4o$2b7o5b2o2bo4b10obob
o8b4o4bo$26b7obo2bo4bo2b8o$b7o15bo2b7obo2bo4b2ob5o$6b2o6bo7bobo4b4obo
2bo7b5o$6b2o13b2o2b2o7bo2bo8b4o$21b2o5b6o3bo6bo4b2o2bo$3b2o5b6o6bo14bo
5bob2o5bo$4bo5b2o4bo5bo15bo4bo4b4o$b5o6bo4bo4bo13b2o4!

Code: Select all

# rotation, view at  at step size of 6
x = 30, y = 33, rule = B06/S67:T60,60
2$4b3obobo4bo2bobo3bo$11b2ob3o2bo2b2o$4bob5ob2o4bo2bo2bo$5b2o3bo2bobo
3bobobo$4b5o5bob3obob3o$12bo2b2ob2o2b2o$5b2ob3ob2obo3b5o$4bo3bobobobo
3bobobo$7bo2bobobobobob2obo$4b2ob4obob2obo2bobobo$6b5o2bob2o4b2obo$4b
2obo4bo4b2o3bobo$4bobobo4b3o3b5o$7b2o2b4ob6o$5b2o2bob2o3b3ob2o2bo$4bo
3bo3bobo2bob2o2bo$6b3o4bob4o3bo$6bob4o2bobo5b2o$4bo3bob2o2bo2bo3bo$4bo
bobob2obo2b2o2bo$4bo2b4o2bo2b2o2bo2bo$5b4obo2b3ob4obo$4bo4b2o4b5ob2obo
$6bobobob3ob2obo2bo$5bo3bo3b3ob5obo$8b6o3bo3b2o$4b4obo3b2o2b2o$4b3o3b
2obob4ob2o2bo!

Code: Select all

x = 30, y = 30, rule = B1568/S012356:T30,30
o2b4o2b2obobobo5b3ob3o$2ob8o5bo3b2o3bob3o$b2o2b7obo2bobo5b2ob3o$3o5bo
5bo4b3obo2b4o$2o2b2o4bo4b2o7bobo2bo$8ob7obo2b3obob3o$obo2b2o3bob2o2bob
o2b2o2b3o$o2bo4b2o3bob3o5b2obo2bo$o4bobo2b6o2b3o3bo4bo$o2b2o4b10obo2b
3o2bo$2o4b2o2b7obo2bo7bo$2o7bob4obo2bo3b3obobo$2ob3ob9o3b3o$8b5o2bo2b
4o3b3o$o6bo5bob2o6b4o$2ob2obo3bo4b2o7b4o$4b2obo3bob5obob2o2bo2bo$o2b2o
2bobob2o4b2ob3obo$o2bo8bo2b3o2b5o4bo$ob2obob2obo7b2obo4bo$ob2obo3b2o3b
2o2bo4bo4bo$7b2ob2obobobo5bobo$bobob2o4b7o2b2obo3bobo$2bo2bobobo4bob3o
bo2bo2bo$4b2o5bobo2bobobo5bo$o2b2o2bob2obobo3bo3bobo2b3o$b5o2b3o2bo3bo
bobobo2bob2o$3b3obo3b3obo6b2o2bo2bo$2bo5b4o4bo3b2ob2obo$ob3obo2bob2obo
2bobo4b3o2bo!

MISCs:

Code: Select all

x = 53, y = 53, rule = B04568/S068
obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobob
obobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobob
obobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobob
obobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobob
obobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobob
obobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobob
obobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obob
obobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobob
obobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobob
obobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobob
o$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobob
obobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobob
obobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobob
obobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobob
obobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobob
obobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobob
obobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$ob
obobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobob
obobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobob
obobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobob
obo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobob
obobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobob
obobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobob
obobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobob
obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobob
obobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobob
obobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$
obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobob
obobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobob
obobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobob
obobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobob
obobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobob
obobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobob
obobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obob
obobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobob
obobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobob
obobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobob
o$obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobob
obobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobob
obobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobob
obobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo!

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Re: Use Smoothiness to classify rules

Post by shouldsee » August 2nd, 2016, 12:47 pm

Gliders (rareness depends on the rule):

Code: Select all

x = 7, y = 4, rule = B0237/S012
2o3b2o3$2bobo!

Code: Select all

x = 5, y = 5, rule = B01234678/S0346
bobo$2obo$bob2o$2obo$bobo!

Code: Select all

x = 11, y = 3, rule = B3678/S0346
b2o$b5o!

Code: Select all

x = 4, y = 4, rule = B03578/S0124678
obo$3bo$2o$bobo!

Code: Select all

x = 4, y = 5, rule = B3468/S03
bo$bobo$o2bo$o2bo$2bo!

Code: Select all

x = 4, y = 5, rule = B01247/S0135
2bo$2o$2obo$2o$2bo!

Code: Select all

x = 40, y = 61, rule = B01245/S235
21$14b4o$13bob2obo$12bob4obo$11bob6obo$12b8o$12b8o$12b8o$12b8o$11b10o$
11b10o$10b12o$10b12o$10b2ob7o$10bob7obo$12b7obo$12b7obo$12b7obo$12b7ob
o$10b10obo$11b10o$9bob12o$10b11obo$9b11o$9b11o$9bob9o$12b8o$12b6o!

Code: Select all

x = 3, y = 6, rule = B0126/S25
o$2bo$obo$obo$2bo$o!

Code: Select all

x = 11, y = 13, rule = B368/S024578
5$4bo$3bobo$2bo$3bo!

Code: Select all

x = 5, y = 3, rule = B013/S4
3o$4bo$3o!

Code: Select all

x = 3, y = 5, rule = B023/S124
3o2$b2o2$3o!

Code: Select all

x = 6, y = 4, rule = B013457/S1234
5bo$6o$2b3o$4bo!

Code: Select all

x = 35, y = 39, rule = B0123/S16
12$4bo15bo$6b14obo$6b14obo$4bo15bo14$12bo$11bobo$14bo$14bo$11bobo$12bo
!

Code: Select all

x = 3, y = 6, rule = B01346/S124
2bo$bo$o$o$bo$2bo!

Code: Select all

x = 24, y = 27, rule = B3458/S0124678
24o$24o$24o$24o$24o$24o$24o$24o$24o$24o$8obob13o$24o$8o4b12o$24o$24o$
24o$24o$24o$24o$24o$24o$24o$24o$24o$24o$24o$24o!

Code: Select all

x = 24, y = 28, rule = B01347/S0234
3$10bo$9bo2$9bo$10bo6$4bo$4b7o$3b8o$3b8o$4b7o$4bo!

Code: Select all

x = 4, y = 5, rule = B357/S347
2bo$bobo$3o$bobo$3bo!

Code: Select all

x = 4, y = 3, rule = B0137/S14
o2bo$o2bo$4o!

Code: Select all

x = 5, y = 6, rule = B0138/S0125
bobo3$o3bo2$bobo!

Code: Select all

x = 6, y = 7, rule = B38/S13568
o3bo$o3bo$o3bo$bobo$2ob2o$b3o$b3o!

Code: Select all

x = 7, y = 7, rule = B01234678/S015
3$2o2bo$2b2o$b4o!

Code: Select all

x = 3, y = 4, rule = B01268/S25
o$b2o$b2o$o!

Code: Select all

x = 3, y = 5, rule = B023/S124
obo$o2$o$obo!

Code: Select all

x = 12, y = 9, rule = B01245678/S01345
b2o$4o$2bo$bobo3$9b3o$9b3o$10bo!

It's possible for patterns to modify the topology of the space in a complex manner

Code: Select all

x = 50, y = 50, rule = B1245678/S01568:T50,50
b2ob2obobob4o3b6obob3obobob5obobobobo$11o2b5o2b8o3bobo2b2o2b4obo2b2o$b
3o3b4o2b2o4b11obob2ob9obobo$16ob2obob8obob5ob4obobobo$b3o3bo2b2ob2obob
3obob2ob2obob9obob3ob2o$o2b5ob12obobobobobobo2b4obobob3o$ob2o3bo2bob9o
bobobobobob4o2b3o7b2o$b3ob3o4b7obobobobobobob5obo3b6o$3ob4ob2o3bo2b4ob
obobobob3obob6o6b2o$bobo2bobo3bobobo4b6ob2obobobobob2ob6o$2o3b6o2bob
11obobobobobobob4o2bobobo$ob9ob3o7b5o2bobob4ob6obobobo$13o2b7obobo3bob
6obob6obobo$2o2b7obob3o4b5obobobob2obobob9o$ob2o2b4o2bob3ob5o2bobobobo
bob3ob5o2bo$ob8ob2obo2bo2bo2b6o2bobo3b13o$2bo2bob4ob3o2bob4o3b4obobob
9obo$4o2bo3bob2obob15obo4bob5ob4o$3b2ob7obobo3bo6b2o4b8o2b2o4bo$6o6bo
2b13ob4obo5b2ob2ob3o$b12o2bo7bobobob2o3bob9o3b2o$ob4o11b5ob5o2b5ob2o2b
2obob3o$2o2b13obo2bob8o5b10o2b2o$7o9bobob4obo2b8o4b9o$o3bo2b8obobob3ob
4obo7b3o3b2ob4o$11obobobob19o3bobob3o2bo$7obob8o3b3obob2o8b3o2b2o2b3o$
2ob2ob3ob6obob3o2b13o4b3ob5o$2ob4o3b3obob5obo3b5o5b8obob3o$2ob4ob4o3b
2ob2obobob2o2b7obo3b3ob5o$3obobo2b7ob8o2bo3bo3b2ob2obob4ob2o$3ob8obobo
b4ob2ob5obobo3bob11o$4o7bobob2ob6ob5obob5obob2ob4obo$b2ob8obobob4o3bob
2o2b2o5b6o4b3o$2ob2o6b5ob2ob8ob2ob10ob3o2b2o$b2obob13obo3b8o4bo2b7o2bo
$obobobob3ob6obob6ob8o2bob3o4b3o$obobob5obob4obobo2b3ob9ob5obo3b2o$obo
bob5o2b3o2b2ob4ob2obobo6b2ob8o$ob9o2b2ob2ob6ob4obob2o2b12o$b6o3b2o4b2o
b5obo4b4ob5ob5o2bo$5ob4ob9o2b2ob15o2bob3obo$8ob2o7bo3bob4o2b3o2b2o2b2o
2b2o3b2o$2ob2obob15obob12ob2ob8o$bob2obobo11bobob8ob4obo3b3o3b2o$b2obo
bob13obob4ob4ob3o2bobob4ob2o$obobobobo9b3obob2ob2o3bob16o$obobobobob3o
b4ob2obob2ob3o2b2obob7ob2ob2o$obobobobob3obo5bobob2ob5obobob4o3b6o$obo
b2obo2bobobob5ob3obob6obobobob6ob2o!
Last edited by shouldsee on August 27th, 2016, 10:14 pm, edited 2 times in total.

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Re: Use Smoothiness to classify rules

Post by shouldsee » August 4th, 2016, 12:21 pm

triphasic

Code: Select all

x = 22, y = 24, rule = B045678/S01568:T100,100
2o4b4o2b2obob2o2bo$b3ob2o2b2ob3ob2obo$ob3obobo2b2o3bob3o$b2obo2b2o5b3o
3b2o$5b2obo4b3obobo$bo2bo3bo9bobo$2obo2bob3obobob4obo$b2o5b4o4b2ob2o$b
2ob2o5bo3b3o2bo$o2b8obo3b3ob2o$o3b2o5bobo3bob2o$5bo5b4obob3o$2ob2obo3b
obobo4b2o$3o2bobo2b5obobo2bo$2obob2obobob2o4bo2bo$3ob2ob3o3bobob2o$7ob
o2bo5b5o$ob2o3b6o2bobo$b3o5b3ob6ob2o$b3o2b3o2b3obo3b2o$3b2o3bobo3b2obo
3bo$bo2b2o3b5o3b2ob2o$2o2bobo4bob2ob6o$o2bobob2o2b2obo3bo2bo!

Code: Select all

x = 32, y = 32, rule = B013/S1236:T100,100
2bo4bobo2bobo2bo3bob3o3b2o$o3b5o5b2o2b2o2b2obob2obo$4bobo2b2o2bo2b2o2b
4o3bo3bo$b2ob3o2bob8obobob4o2bo$4ob3obob2o4bob4o2bobob3o$obo2b6o4bob2o
5b2o2b2o$10b2o3bo4bo2bo3b2o$5b2obo2bob3obob2ob2ob4o$2b3o4b2o2b4obo2b5o
b3o$b2obob3o2bo3b2ob6o3b3o$2o2bo4bobobobo6b4o2b2o$2o4b2obob3o3b4o3b5o
2bo$o3bo2b2ob3o2b3o4b3o5bo$bo2bobob3o2b3o3bo4b2ob2o2bo$o2bo3bobo2b2obo
2b5o2bo2b2obo$ob3ob2o3bobobo4bo2bob2o2b2o$ob2o4bo4b2o4b2o6bo2bo$obo3b
4o2b2ob7o2b2o2b2o$ob2obobo4bo2b2o3b5ob2ob3o$o2b4o7bobo3bo2b3o2b2obo$4b
obobo5bob5o3bo2bo3bo$b3o5b2o3b3o2b3o6bo$bob6o4bobo2bo5bob2o2b2o$o5b3o
5bobob2obob2o4bobo$bo2bo2bobo3bobob3o3b4o2b2o$2obobob2o4bobob3o2b2ob3o
b3o$bo2bo5b3o5b2obo4b3o2bo$obo2bo2b2o3bo2bo2b3ob2o5bo$5b3obob2o3bo2b4o
b3obo$2bo2b3obo3bob2obob2obob2o3b2o$2o3b2ob2o4b3o2bobob3o3bo$ob2obo2bo
2bo3b5o2bo2bo2bo!
Last edited by shouldsee on August 9th, 2016, 3:02 pm, edited 1 time in total.

Bullet51
Posts: 536
Joined: July 21st, 2014, 4:35 am

Re: Use Smoothiness to classify rules

Post by Bullet51 » August 6th, 2016, 5:56 am

shouldsee wrote:
The next question, naturally , is then how comes that some rules transmits at specific frequencies and other rules have a distributed frequency.
Good question!
It seems that amoeba-like and replicator-like dynamics have a distributed frequency. I'm not sure what kind of rules transmits at a specific frequency, but B35S13 may be a good choice.
Is it OK for you to upload the program for computing the values?
Still drifting.

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Re: Use Smoothiness to classify rules

Post by shouldsee » August 6th, 2016, 6:39 am

Bullet51 wrote:
shouldsee wrote:
The next question, naturally , is then how comes that some rules transmits at specific frequencies and other rules have a distributed frequency.
Good question!
It seems that amoeba-like and replicator-like dynamics have a distributed frequency. I'm not sure what kind of rules transmits at a specific frequency, but B35S13 may be a good choice.
Is it OK for you to upload the program for computing the values?
As I continue to explore the implication of frequency, it appears the autocorrelation profile is not constant throughout the evolution, though it does appear that some rules show a robust profile.

see attached figure 1&2 for a comparison between complex and chaotic rules.

On a such observation, it appears dangerous to take only one window and calculate the autocorrelation profile (since it would only be a random sample from a set of possible configurations.) Trying to reconcile this randomness, I sought a global parameter to measure the distribution of such configurations. Originally I tried to take pair-wise distance between a series of autocorrelation profiles and analyse the resultant distance matrix, (effectively a return map). And it was quite fun to analyse it.

But it later comes to me that, if I am making return map only, why should I take the extra step of calculating autocorrelation profile? I started to measure pair-wise distance between the moving averages of entropy directly, and the resultant map appears powerful in discriminating between the rules.

figure3
Image
figure4
Image
figure5
Image


After that, it was all about how to extract parameters from the return map optimally. I tried to tell my laptop to identify the true tracks/return points by applying a convolution. But there is really much more you can do with it.

About data collection, I used a matlab script. The gui is pretty dirty and the code quite messy and probably not easy to use. But I will post them here anyway if anyone wants a read.
Attachments
CA.tar.gz
matlab scripts
(8.42 KiB) Downloaded 150 times
figure2
figure2
chrule3.jpg (63.77 KiB) Viewed 12099 times
figure1
figure1
corule2.jpg (59.73 KiB) Viewed 12099 times

User avatar
ygh
Posts: 47
Joined: March 18th, 2016, 4:47 pm

Re: Use Smoothiness to classify rules

Post by ygh » August 8th, 2016, 8:19 pm

Do B36/S0124567!
It's not explosive, but it is REALLY close.

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

Re: Use Smoothiness to classify rules

Post by shouldsee » August 9th, 2016, 2:54 pm

This post is reminiscent of the 2nd post


Oscillators/sparks:

Code: Select all

x = 6, y = 6, rule = B01234/S146
2b2o$2b2o$6o$6o$2b2o$2b2o!
341 gen spark

Code: Select all

x = 4, y = 4, rule = B01234/S146
$b2o$b2o!

Code: Select all

x = 5, y = 4, rule = B0136/S0
bobo$b2o$b3o$5o!

Code: Select all

x = 30, y = 30, rule = B3458/S678
30o$13o4b13o$30o$11o8b11o$30o$9o2b8o2b9o$30o$8o14b8o$7ob14ob7o$5obob4o
6b4obob5o$5obob14obob5o$3ob3ob3o8b3ob3ob3o$3ob3obobob6obobob3ob3o$obob
3obobob6obobob3obobo$obob3obobob6obobob3obobo$obob3obobob6obobob3obobo
$obob3obobob6obobob3obobo$3ob3obobob6obobob3ob3o$3ob3ob3o8b3ob3ob3o$5o
bob14obob5o$5obob4o6b4obob5o$7ob14ob7o$8o14b8o$30o$9o2b8o2b9o$30o$11o
8b11o$30o$13o4b13o$30o!

Code: Select all

x = 61, y = 66, rule = B12458/S0234678:T61,66
61o$61o$61o$61o$61o$61o$61o$26o4b31o$26o4b31o$26o4b31o$26o4b31o$26o4b
31o$26o4b31o$26o4b31o$26o4b31o$26o4b31o$26o4b31o$16o24b21o$16o24b21o$
14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o
2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b
10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$4o48b9o$4o48b9o$4o
48b9o$4o48b9o$4o48b9o$4o48b9o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$
14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o
2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b10o4b10o2b19o$14o2b
10o4b10o2b19o$16o24b21o$16o24b21o$26o4b31o$26o4b31o$26o4b31o$26o4b31o$
26o4b31o$26o4b31o$26o4b31o$26o4b31o$26o4b31o$26o4b31o$61o$61o$61o$61o$
61o$61o$61o$61o$61o!

Code: Select all

x = 38, y = 61, rule = B0123456/S2347
6$19bo2bo$20b2obo$20b3obo$19bob3obo$20bob4o$21bob2obo$22b2o2bo$24b3o
11$18bo2bo$17bob2o$16bob3o$17b3obo$17b2obo$16bo2bo15$14bo2bo$15b2obo$
15b3obo$14bob3o$13b2o2b2o$13bob2o2bo$13b3o!

Code: Select all

x = 68, y = 60, rule = B01248/S012345
6$13b4o$10b3o4b3o$13b4o$9b5o3b4o$13b5o2bobo$10b2obobob4obo$8b2obobob2o
3bob2o$10b2obobob4obo$7b3obobobobo$11bobobob3o$7b7obo$15b4o$6b9o$15b4o
$6b10o$6bo8bob3o2bo$5bob9obobobo$3bobobo7bobobob2o$3bobob9obobobo32bob
o$bobob2o8bobobo2bo30b5o$3bobob9obo$3bobobo7bobo31bob9o$5bob7obo31bobo
$27bo4bo14bob12obo$7b9o9bobobobo11bobobobo10bobobo$25bobobob2o9b2obob
3ob8obobobo$7b8o10bobobobo10b4ob5obo4bobobobobo$25bobobo11bo4b13obobob
obo$8b7o12bobo10b2ob12obobobobobobo$41bob12obobobobobobo$10b4o26b2ob
14obob3obo$38bobobob15o4bo$38bobob21o$36bobob18o$38bobob21o$38bobob19o
$36bobob22o$36bob22obo$33bobob2ob21o$31bobobobobob10o2b8o$31bobobobobo
b13ob5o$31bobobobobob9o5bobobo$31bobobobobobobob2ob8obobobo$29bobobobo
bobobobo3bo7bobobobo$29bobobobobobobob13obobobo$29bobobobobobobobo11bo
bobobo$29bobobobobobobob13o2bobo$31bobobobobobobo11b4obo$35bobobobob
13o2bobo$35bobobobobo10bob3o$37bo5bob8obo2$47b4o!
Agar Crawler:

Code: Select all

x = 48, y = 63, rule = B034567/S18:T48,63
obobobobobobobo8bo8bobobobobobobobo$obobobobobobobob5ob3ob5obobobobobo
bobobo$obobobobobobobobob3o5b3obobobobobobobobobo$obobobobobobobob5ob
3ob5obobobobobobobobo$obobobobobobobo2b3o7b3o2bobobobobobobobo$obobobo
bobobobobobob7obobobobobobobobobobo$obobobobobobobobo13bobobobobobobob
obo$obobobobobobobob15obobobobobobobobo$obobobobobobobob15obobobobobob
obobo$obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobob
obobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobob
obobobobo$obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobob
obobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobob
obobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo$obobobob
obobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobob
obobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo$obob
obobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobob
obobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo$
obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobob
obobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobob
obo$obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobob
obobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobob
obobobo$obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobob
obobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobob
obobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo$obobobobob
obobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobob
obobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo$obobob
obobobobobobobobobobobobobobobobobobobobo$obobobobobob23obobobobobobo$
obobobobobobo21bobobobobobobo$obobobobobobo2b17o2bobobobobobobo$obobob
obobobo21bobobobobobobo$obobobobobobob19obobobobobobobo$obobobobobobob
o17bobobobobobobobo$obobobobobobo2bobob9obobo2bobobobobobobo$obobobobo
bobobo17bobobobobobobobo$obobobobobobob19obobobobobobobo$obobobobobobo
bo17bobobobobobobobo$obobobobobobo2bob3obobobob3obo2bobobobobobobo$obo
bobobobobobo17bobobobobobobobo$obobobobobobob19obobobobobobobo$obobobo
bobobobo17bobobobobobobobo$obobobobobobo2bobobobobobobobobo2bobobobobo
bobo$obobobobobobobo17bobobobobobobobo$obobobobobobob19obobobobobobobo
$obobobobobobobo17bobobobobobobobo$obobobobobobo2bobobob5obobobo2bobob
obobobobo$obobobobobobobo17bobobobobobobobo$obobobobobobob19obobobobob
obobo$obobobobobobobo17bobobobobobobobo$obobobobobobo2bobo3bobobo3bobo
2bobobobobobobo$obobobobobobobo17bobobobobobobobo$obobobobobobob19obob
obobobobobo$obobobobobobobo17bobobobobobobobo$obobobobobobo2b17o2bobob
obobobobo!

Short-lived patterns/ strong but imperfect attractors (possibly perfect in closely related rules):

Code: Select all

x = 25, y = 58, rule = B0134/S0134
3$7b5o$9b2o$4bob3ob2o$4b3o10$10bob2o$11b2o$9b2ob2o12$8b2ob2o$10b2o$8b
2ob2o11$8b2ob2o$9b3o$8b2ob2o!

Code: Select all

x = 70, y = 35, rule = B01245/S1245
4$55b3o$26bobo25bobobo$28bo25b5o$22b5obo25b5o$5bo17bo30b2ob2o$2b7o13b
4o30bo$3b5o13b5o13bo$3bobobo13b6o10b2ob2o14bo$4b3o14b4obo10b5o12b2ob2o
$21bobobo11b5o12b5o$22b3o12bobobo12b5o$38b3o13bobobo$55b3o3$b4o$ob4o$4obo$ob4o$b4o!
!

Code: Select all

x = 7, y = 6, rule = B012457/S01245
2b3o$bobobo$ob3obo$7o$7o$b5o!
Puffers

Code: Select all

x = 14, y = 44, rule = B013478/S0234
2$3bo4bo$4b3obo2bo$5b3ob2o$4b2obo$6b2o3bo$6bo$6bo3b2o2$3bo4bo$6bo$8bo$
5bo$6bobo$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$
4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$4b4o$3b6o$5b2o!

Code: Select all

x = 39, y = 52, rule = B0123458/S12356
7$10b4o$8bo2b2o2bo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4o
bo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob
4obo$8bob4obo$8bob4obo10b6o$8bob4obo9bo$8bob4obo7b8obo$8bob4obo6b11o$
8bob4obo6b11o$8bob4obo7b8obo$8bob4obo9bo$8bob4obo10b6o$8bob4obo$8bob4o
bo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bob
4obo$8bob4obo$8bob4obo$8bob4obo$8bob4obo$8bo2b2o2bo$10b4o!
Guns:

Code: Select all

x = 26, y = 21, rule = B0178/S01
3$2b2o$2b2o$20b2o$19b3o$19b3o$8b2o9b3o$8b2o9b3o$20b2o$14bo$6bo5bo3bo$
6bo4bo4bo$14bo2$2o$2o!

Code: Select all

x = 5, y = 5, rule = B012368/S1236
bobo$bobo$5o$bobo$bobo!
Last edited by shouldsee on August 28th, 2016, 8:45 am, edited 4 times in total.

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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 11:37 am

BlinkerSpawn wrote:Maybe instead of looking at variance between neighbor counts, look at variance between neighborhoods within neighbor counts?
For instance, a relatively orderly B2 rule would likely experience a lot more B2a or B2e than other B2 transitions.
Yes I tried to include orientation into account but it multiplies the number of variable by 45, and consider this is a O(n^2) complexity..... It's not clear how much symmetry we should impose on this scheme. The less symmetry in the prior, the harder the computation. So I guess we have to impose some symmetry to reduce the computation power required.
Bullet51 wrote:
It turns out that chaotic rules have weak tangling, and complex rules have moderate tangling.Maybe we are going off-topic...

If we just use the crude estimation, rules with glider usually has an average tangling around 0.25-0.20.

Yes it's quite off topic I guess we should switch to the "smoothness" post.If we just use the crude estimation,
Another problem plaguing the result is the existence of trending, often 2 counts are detected to co-vary just because of the overall trend where an area of vain is converted to populated area, but this isn't the kind of covariation we are going for.
For example, the colored rules have gliders, but others has a similar meanCov

Code: Select all

rule            meanCov
----rules with glider
B01345/S1235	0.2563795076
B0126/S025	0.2545034158
B0136/S013	0.2508132105
B012346/S12347	0.2369579273
B01246/S2345	0.2340526527
B0246/S1234678	0.1897935461
B0123478/S13456	0.1886938569
B023/S3	0.1839539771
------rules without
B0136/S013	0.2508132105
B01235/S1235	0.2501014408
B01235/S1235	0.2501014408
B38/S0137	0.2481482123
B38/S0137	0.2481482123
B38/S0137	0.2481482123
B048/S12348	0.2474349491
B048/S12348	0.2474349491
B048/S12348	0.2474349491
B048/S12348	0.2474349491
B123467/S13678	0.2451007682
B123467/S13678	0.2451007682
B123467/S13678	0.2451007682
B123467/S13678	0.2451007682
B38/S1235	0.2441705062
B38/S1235	0.2441705062
B38/S1235	0.2441705062
B38/S1235	0.2441705062
B0123468/S0125	0.2432472846
B0148/S012346	0.2421045013
B0148/S012346	0.2421045013
B0148/S012346	0.2421045013
It's also possible to find glider-allowing rules outside this interval. For example many aforementioned replicator/moving head-allowing rules are not here yet. I am curious where are they on the list
Last edited by shouldsee on August 11th, 2016, 1:30 pm, edited 3 times in total.

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Re: Use Smoothiness to classify rules

Post by BlinkerSpawn » August 11th, 2016, 11:40 am

shouldsee, in the 'Rules with Abnormally Common High-Period Oscillators' thread, wrote:
BlinkerSpawn wrote:Maybe instead of looking at variance between neighbor counts, look at variance between neighborhoods within neighbor counts?
For instance, a relatively orderly B2 rule would likely experience a lot more B2a or B2e than other B2 transitions.
Yes I tried to include orientation into account but it multiplies the number of variable by 45, and consider this is a O(n^2) complexity.....
What I had meant to say there is that you only compare each neighborhood to the other neighborhoods with the same neighbor count. So instead of comparing the transition classes with each other directly, you compare the transitions within each class to the other in the same class using statistical techniques and then manipulate the results accordingly.
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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 11:47 am

BlinkerSpawn wrote:
shouldsee, in the 'Rules with Abnormally Common High-Period Oscillators' thread, wrote:
BlinkerSpawn wrote:Maybe instead of looking at variance between neighbor counts, look at variance between neighborhoods within neighbor counts?
For instance, a relatively orderly B2 rule would likely experience a lot more B2a or B2e than other B2 transitions.
Yes I tried to include orientation into account but it multiplies the number of variable by 45, and consider this is a O(n^2) complexity.....
What I had meant to say there is that you only compare each neighborhood to the other neighborhoods with the same neighbor count. So instead of comparing the transition classes with each other directly, you compare the transitions within each class to the other in the same class using statistical techniques and then manipulate the results accordingly.
Okay gotcha, so you meant to compare within transition classes rather than between. But say I am comparing B2 transitions, but B2a might be tangling with B3a, this would not be reflected if the comparison is local.... There is no constraint that require tangling to be within a class, so a detailed global test would be preferred I guess.

But it's worth trying, it's the only way to test whether this would work.

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Re: Use Smoothiness to classify rules

Post by BlinkerSpawn » August 11th, 2016, 12:03 pm

shouldsee wrote:Okay gotcha, so you meant to compare within transition classes rather than between. But say I am comparing B2 transitions, but B2a might be tangling with B3a, this would not be reflected if the comparison is local....
I can see how common attractors crossing multiple classes (i.e. almost all of them) might be misinterpreted in the two-phase comparison, but then in most cases the transitions utilized by said attractors would inevitably comprise the majority of the transitions in each class. (right?)
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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 12:11 pm

BlinkerSpawn wrote:
shouldsee wrote:Okay gotcha, so you meant to compare within transition classes rather than between. But say I am comparing B2 transitions, but B2a might be tangling with B3a, this would not be reflected if the comparison is local....
I can see how common attractors crossing multiple classes (i.e. almost all of them) might be misinterpreted in the two-phase comparison, but then in most cases the transitions utilized by said attractors would inevitably comprise the majority of the transitions in each class. (right?)
Sorry I am not quite sure about your point still....need a bit more explanation... Common attractors would be re-iterated a lot so as to create tangling between transitions, (i.e. the transitions they utilise would be enriched synchronously.)

But I am not sure about '2-phase' comparison and the "said attractor"
Last edited by shouldsee on August 11th, 2016, 12:14 pm, edited 1 time in total.

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Re: Use Smoothiness to classify rules

Post by Bullet51 » August 11th, 2016, 12:13 pm

shouldsee wrote: For example, the colored rules have gliders, but others has a similar meanCov

Code: Select all

rule meanCov
B01345/S1235	0.2563795076
B0126/S025	0.2545034158
B0136/S013	0.2508132105
B012346/S12347	0.2369579273
B01246/S2345	0.2340526527
B0246/S1234678	0.1897935461
B0123478/S13456	0.1886938569
B023/S3	0.1839539771
B0136/S013	0.2508132105
B01235/S1235	0.2501014408
B01235/S1235	0.2501014408
B38/S0137	0.2481482123
B38/S0137	0.2481482123
B38/S0137	0.2481482123
B048/S12348	0.2474349491
B048/S12348	0.2474349491
B048/S12348	0.2474349491
B048/S12348	0.2474349491
B123467/S13678	0.2451007682
B123467/S13678	0.2451007682
B123467/S13678	0.2451007682
B123467/S13678	0.2451007682
B38/S1235	0.2441705062
B38/S1235	0.2441705062
B38/S1235	0.2441705062
B38/S1235	0.2441705062
B0123468/S0125	0.2432472846
B0148/S012346	0.2421045013
B0148/S012346	0.2421045013
B0148/S012346	0.2421045013
It seems that Meancov statistic is too rough:
1.png
1.png (16.77 KiB) Viewed 11972 times
The characteristic of the correlation matrix is quite different, even when the Meancov is similar.
Still drifting.

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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 12:17 pm

Bullet51 wrote: It seems that Meancov statistic is too rough:
1.png
The characteristic of the correlation matrix is quite different, even when the Meancov is similar.
The mean cov is definitely not enough. I did try spectral clustering/ listing the eigenvalue of the matrix, but it was fruitless and I don't really understand these tools perfectly to use them. I guess we can still try to partition the covariation matrix.

Ultimately we need to produce some scalar/logical output to denote the "complexity/emergence" of this rule. Mean cov is only a very crude way to describe the complexity of a dynamics for a specific period.

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Re: Use Smoothiness to classify rules

Post by Bullet51 » August 11th, 2016, 12:28 pm

BlinkerSpawn wrote:but then in most cases the transitions utilized by said attractors would inevitably comprise the majority of the transitions in each class. (right?)
Right. In B4S2, the s2e and s2a transitions dominate, and in B3S26, s2i and s2c dominate.
Last edited by Bullet51 on August 11th, 2016, 12:50 pm, edited 1 time in total.
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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 12:32 pm

Bullet51 wrote:
BlinkerSpawn wrote:but then in most cases the transitions utilized by said attractors would inevitably comprise the majority of the transitions in each class. (right?)
Perhaps not, since they co-vary just because of the overall trend where an area of vain is converted to populated area.
1.png
In B3S236 the attractors are mainly blinkers, but mostly all of the transitions correlates.
We should not only include the self-perpetuating attractors, but also the transient ones. For example, if a wavefront is eating up the vain, it might prefers a combination of neighbourhoods. In the case of B3S236 I would guess the chaotic mess is the source of covariation.

So one possible way to improve the algorithm is by taking into account the overall trend of the global dynamics. In other words, we want covariation/tangling, but not at the transient front of a conversion wave. We want it to be localised, and not explosive....

On the other hand, these 'bad' rules without gliders sometimes do exhibit localised cooperativity, but on some other fabric of their preference instead of the usual fabric of vain. We just don't have suitable tools yet to systematically studying such emergent behaviour due to a lack of regularity in the underlying fabric.
Last edited by shouldsee on August 11th, 2016, 1:05 pm, edited 3 times in total.

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Re: Use Smoothiness to classify rules

Post by BlinkerSpawn » August 11th, 2016, 12:38 pm

shouldsee wrote:Sorry I am not quite sure about your point still....need a bit more explanation... Common attractors would be re-iterated a lot so as to create tangling between transitions, (i.e. the transitions they utilise would be enriched synchronously.)

But I am not sure about '2-phase' comparison and the "said attractor"
"2-phase" referred to the plan of analyzing variance within classes (Phase 1) and then combining the results into a statistic (Phase 2)
"said attractors" referred to the "common attractors" ("said" in this context is similar to "aforementioned", "described previously", and similar words/phrases)
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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 12:46 pm

BlinkerSpawn wrote:
shouldsee wrote:Sorry I am not quite sure about your point still....need a bit more explanation... Common attractors would be re-iterated a lot so as to create tangling between transitions, (i.e. the transitions they utilise would be enriched synchronously.)

But I am not sure about '2-phase' comparison and the "said attractor"
"2-phase" referred to the plan of analyzing variance within classes (Phase 1) and then combining the results into a statistic (Phase 2)
"said attractors" referred to the "common attractors" ("said" in this context is similar to "aforementioned", "described previously", and similar words/phrases)
Okay, "aforementioned" is a lot easier to understand.

I am really skeptical about the advantage of the 2-phase statistics. Imagine there is really such tangling, then we can detect them in a global covariation test by exclude rotat4reflect symmetry when counting the neighborhoods. The aforementioned 2-phase co-variation test is like taking only the diagonal squares of this larger matrix, which seems very dangerous to me (though maybe faster by reduce O(n^2) to O(n))

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Re: Use Smoothiness to classify rules

Post by Bullet51 » August 11th, 2016, 1:09 pm

When applying eigendecomposition to the covariance matrix, it seems that the first eigenvalue is very large, compared to the second eigenvalue.

Code: Select all

Rule               1st eigenvalue        2nd eigenvalue
--------------------------------------------------------
Move(B368S245)     46.22                 1.55
B3S237             32.25                 2.14    
B3S125             40.66                 1.40
B3S12              39.41                 2.42

DotLife(B3S023)    26.41                 2.40
Seeds(B2S)         20.45                 2.87            
Gnarl(B1S1)        17.26                 7.73       (3rd 2.79)
Last edited by Bullet51 on August 11th, 2016, 1:16 pm, edited 1 time in total.
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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 1:15 pm

Bullet51 wrote:When applying eigendecomposition to the covariance matrix, it seems that the first eigenvalue is very large, compared to the second eigenvalue.

Code: Select all

Rule               1st eigenvalue        2nd eigenvalue
--------------------------------------------------------
Move(B368S245)     46.22                 1.55
B3S237             32.25                 2.14    
DotLife(B3S023)    26.41                 2.40
B3S125             40.66                 1.40
B3S12              39.41                 2.42
Seeds(B2S)         20.45                 2.87            
Gnarl(B1S1)        17.26                 7.73       (3rd 2.79)
Can you include some noisy sample please?

How many soup are you cooking for average? And what's the time span of each soup?
Last edited by shouldsee on August 11th, 2016, 1:17 pm, edited 1 time in total.

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Re: Use Smoothiness to classify rules

Post by Bullet51 » August 11th, 2016, 1:17 pm

shouldsee wrote: Can you include some noisy sample please?
I'm not sure what does "noisy" means. Perhaps chaotic?
How many soup are you cooking for average?
One :lol:
The size of the soup is 600x600.
And what's the time span of each soup?
400 gens.
Last edited by Bullet51 on August 11th, 2016, 1:18 pm, edited 1 time in total.
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Re: Use Smoothiness to classify rules

Post by shouldsee » August 11th, 2016, 1:18 pm

Bullet51 wrote:
shouldsee wrote: Can you include some noisy sample please?
I'm not sure what does "noisy" means. Perhaps chaotic?
How many soup are you cooking for average?
One :lol:
:__:

Yes chaotic ones. Or non-glider ordered ones.

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Re: Use Smoothiness to classify rules

Post by Bullet51 » August 11th, 2016, 1:24 pm

shouldsee wrote: Yes chaotic ones. Or non-glider ordered ones.
Sure:

Code: Select all

Rule          1st eigenvalue        2nd eigenvalue
--------------------------------------------------------    
Chaotic:
B12S01        25.46                 8.72      (3rd 5.29)
B23S12        23.64                 10.61     (3rd 4.55)
B34S25        11.41                 5.05      (3rd 2.76)
B1357S1357    7.07                  3.46      (3rd 2.89)

Non-glider (600x600 soup,1000 gens):
B4678S35678   39.30                 9.78
B345S5        33.06                 9.98
B3S234        32.19                 13.90
B3S03*        45.55                 2.75

*B3S03 is a stable rule.
Still drifting.

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