Bullet51 wrote:A somewhat difficult question: How much information can we extract from the transition matrix?
shouldsee wrote:We can evaluate the reversibility by counting the states with a backward uncertainty near zero. For example, B01367S01 has a big collection of states near Bunc=0. B3S23 has a smaller collection. This reflects the fact that B01367S01 has more spontaneous spaceships/replicators than B3S23.
Bullet51 wrote:shouldsee wrote:We can evaluate the reversibility by counting the states with a backward uncertainty near zero. For example, B01367S01 has a big collection of states near Bunc=0. B3S23 has a smaller collection. This reflects the fact that B01367S01 has more spontaneous spaceships/replicators than B3S23.
The rule B378S126 may be a good sample to test. How many states are there near Bunc=0?
x = 69, y = 220, rule = B0345678/S0158:T69,220
2obo2bobo2bobobobobo2bobo2bobobobobo2bobobobobobobobobobobobobob2obo$
69o2$69o2$bobo2bobo2bobobobobo2bobo2bobobobobo2bobobobobobobobobobobob
obob2obo2$69o2$69o$obob2obob2obobobobob2obob2obobobobob2obobobobobobob
obobobobobobo2bobo$69o2$69o2$obob2obob2obobobobob2obob2obobobobob2obob
obobobobobobobobobobobo2bobo2$69o2$28o5b36o$bobo2bobo2bobobobobo2bobo
2b7obo2bobobobobobobobobobobobobob2obo$29obob37o$30bo$29o3b37o$27b2o3b
2o$bobo2bobo2bobobobobo2bobob2obobob3o2bobobobobobobobobobobobobob2obo
$29bobo$30ob38o$30bo$29obob2ob34o$obob2obob2obobobobob2obobobo2bobo4bo
bobobobobobobobobobobobobo2bobo$29obob37o$30bo$30ob38o$27b2o$obob2obob
2obobobobob2obob9obobobobobobobobobobobobobobobo2bobo$27b2o2bo$69o2$
69o$bobo2bobo2bobobobobo2bobobobo7bobobobobobobobobobobobobobob2obo$
30obobob34o2$69o2$bobo2bobo2bobobobobo2bobob13obobobobobobobobobobobob
ob2obo$28bobobobobo$69o2$69o$obob2obob2obobobobob2obo17bobobobobobobob
obobobobo2bobo$25obobobobobobobob29o2$69o2$obob2obob2obobobobob24obobo
bobobobobobobobo2bobo$23bobobobobobobobobobo$69o2$69o$bobo2bobo2bobobo
bobobo24bobobobobobobobobob2obo$24obobobobobobobobobobob24o2$69o2$bobo
2bobo2bobobobobobobob24obobobobobobobob2obo$26bobobobobobobobobobobo$
69o2$69o$obob2obob2obobobobobobobobo24bobobobobobobo2bobo$29obobobobob
obobobobobob19o2$69o2$obob2obob2obobobobobobobobobob24obobobobobo2bobo
$31bobobobobobobobobobobo$69o2$69o$bobo2bobo2bobobobobobobobobobobo24b
obobobob2obo$34obobobobobobobobobobob14o2$69o2$bobo2bobo2bobobobobobob
obobobobobob24obobob2obo$36bobobobobobobobobobobo$69o2$69o$obob2obob2o
bobobobobobobobobobobobobo24bobo2bobo$39obobobobobobobobobobob9o2$69o
2$obob2obob2obobobobobobobobobobobobobobob24o2bobo$41bobobobobobobobob
obobo$69o2$69o$bobo2bobo2bobobobobobobobobobobobobobobobo23bobo$44obob
obobobobobobobob6o2$69o2$bobo2bobo2bobobobobobobobobobobobobobobobobob
17obobobo$46bobobobobobobobo$69o2$69o$obob2obob2obobobobobobobobobobob
obobobobobobobo13bobobobobo$49obobobobob11o2$69o2$obob2obob2obobobobob
obobobobobobobobobobobobobobob7obobobobobobo$51bobobo$69o2$69o$bobo2bo
bo2bobobobobobobobobobobobobobobobobobobobobo3bobobobobobobo$69o2$69o
2$bobo2bobo2bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
2$69o2$69o$obob2obob2obobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobo$69o2$69o2$obob2obob2obobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo2$69o2$69o$bobo2bobo2bobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$69o2$69o2$bobo2bobo2bobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobo2$69o2$69o$obob2obob2obobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobo$69o2$69o2$obob2obob2o
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2$69o2$69o$b
obo2bobo2bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$
69o2$69o2$bobo2bobo2bobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobo2$69o2$69o$obob2obob2obobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobo$69o2$69o2$obob2obob2obobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobo2$69o2$69o$bobo2bobo2bobobobobobobobobobob
obobobobobobobobobobobobobobobobobobo$69o2$69o2$bobo2bobo2bobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobo2$69o2$69o$obob2obob2obo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobo$69o2$69o2$obo
b2obob2obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2$
69o2$69o$bobo2bobo2bobobobobobobobobobobobobobobobobobobobobobobobobob
obobobo$69o2$69o2$bobo2bobo2bobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobo2$69o2$69o$obob2obob2obobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobo$69o2$69o2$obob2obob2obobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobo2$69o2$69o!
x = 243, y = 12, rule = B12348/S123468:T243,12
96obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobob2o$95bobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobo$94obobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$93bobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobob2o$94obobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$82b2o9bobo
bobobobobobobob5obobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obo$94obobobobobobobobob7obobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobob2o$81b3o11bobobobobobobobob7obobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobo$96obobobobobobobob5obobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobob2o$82b2o13bobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobo$98obobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobob2o$o96bobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo!
shouldsee wrote:To remove the strobing effect, transition is taken every 6 steps.
shouldsee wrote:Sadly, the arm region indicated with red dots doesn't constitute an exclusive area, i.e interesting rules in curated collection are bound to lie in such region, but points in such region are not necessary interesting.
G:Glider-Possible
N:Natural-Glider-Possible
S:Special
A:Ameoba dynamics
F:Fast-Decay
B357/S238 N
B013568/S0123 N
B012358/S01237 G
B3468/S028 G
B01245/S14 G
B0123457/S0126 N
B2346/S124678 S
[The negative rule is b358s01378, which is N]
B0127/S0135 G
B358/S136 N
B01367/S01 G
[Possibly N]
B123568/S123678 S
[The negative rule is b348s148, which is N]
B01347/S13 N
B0127/S0235 G
B2578/S0234678 S
[The negative rule is b37s24578, which is G]
B378/S024678 N
B01237/S236 S
[It has natural puffers, but not natural gliders]
B013678/S0 N
B012456/S023 N
B0123567/S02346 G
[Possibly N]
B378/S02458 G
[Possibly N]
B3678/S135 N
B012467/S1235 N
B358/S12678 N
B12/S12478 S
[Biphasic. May be regarded as complex behaviour]
B37/S0245 N
[Has a 4c/25 glider: b5o$o4bo$o4bo$b5o!]
B3568/S136 N
B012345/S0246 N
B0134568/S0234 N
[The natural ship is actually an infinite class of ships]
B013457/S0123 G
[There are too many replicators]
B013458/S02 G
[There are too many replicators]
B01267/S0125 A
B358/S1267 N
B123478/S24678 S
[The negative rule is b3578s238, which is G, and have a replicator]
B01258/S025 G
[Possibly N]
B024678/S04678 S
[The negative rule is b3567s3578, which is G]
B0134568/S1234 S
[It has natural puffers, but not natural gliders]
B01238/S1246 G
B012/S015 F
B34/S368 F
B012357/S14678 S
[The negative rule is b3578s238, which is N]
B01234567/S035 A
B0123578/S135 A
B01246/S01234678 S
[The negative rule is b3s0135, which is both N and puffer-natural]
B346/S0567 G
B3468/S01 G
[Sometimes explodes]
B012458/S4 A
B0123457/S023678 S
[The negative rule of b347s02, which is G]
B012567/S014 A
[It converges to some strange states]
B348/S037 G
B123458/S024678 S
[Negative of b357s128, which is G]
B012/S145 A
B356/S034 G
[Maybe F]
B1578/S234678 S
[Negative of b378s24568, which is full of gliders]
B0123456/S01235 F
[Has a glider]
B01278/S012468 S
[Biphasic. May be regarded as complex behaviour]
B0138/S4 N
B0123578/S1236 G
[Heavy ameoba dynamics]
B3568/S0146 N
shouldsee wrote:This indicates that we may still need extra dimension to expand this 'arm' region.
x = 16, y = 7, rule = B0126/S015H
5bo6bo$4bo6bo$obobob8o$o2bo2b8obo$bobobob8o$6bo6bo$8bo6bo!
Bullet51 wrote:shouldsee wrote:To remove the strobing effect, transition is taken every 6 steps.
2 steps is enough.
Bullet51 wrote:shouldsee wrote:Sadly, the arm region indicated with red dots doesn't constitute an exclusive area, i.e interesting rules in curated collection are bound to lie in such region, but points in such region are not necessary interesting.
Points in such region, of course, are not necessary interesting, but most of them are interesting:
The region is determined by a neural network.
Bullet51 wrote:shouldsee wrote:This indicates that we may still need extra dimension to expand this 'arm' region.
Surely.
Bullet51 wrote:Would you like to share your program, since I think it's a good idea to use the program to search hexagonal rules:
shouldsee wrote:DId you just used the 3 features I provided?
shouldsee wrote:Or what's the shape recognised by your NN?
shouldsee wrote:Sure. It just took some cleaning work. I have updated the link on the frontpage. Although to apply for hexagonal, you would need to undertake a extensive change.
Bullet51 wrote:shouldsee wrote:Or what's the shape recognised by your NN?
Somewhat hard to say, since I don't know how to plot the surface of f(x,y,z)=0.
Bullet51 wrote:Thanks!
shouldsee wrote:Or what's the shape recognised by your NN?
Bullet51 wrote:[
Points in such region, of course, are not necessary interesting, but most of them are interesting:Code: Select allG:Glider-Possible
N:Natural-Glider-Possible
S:Special
A:Ameoba dynamics
F:Fast-Decay
B357/S238 N
B013568/S0123 N
B012358/S01237 G
B3468/S028 G
B01245/S14 G
B0123457/S0126 N
B2346/S124678 S
[The negative rule is b358s01378, which is N]
B0127/S0135 G
B358/S136 N
B01367/S01 G
[Possibly N]
B123568/S123678 S
[The negative rule is b348s148, which is N]
B01347/S13 N
B0127/S0235 G
B2578/S0234678 S
[The negative rule is b37s24578, which is G]
B378/S024678 N
B01237/S236 S
[It has natural puffers, but not natural gliders]
B013678/S0 N
B012456/S023 N
B0123567/S02346 G
[Possibly N]
B378/S02458 G
[Possibly N]
B3678/S135 N
B012467/S1235 N
B358/S12678 N
B12/S12478 S
[Biphasic. May be regarded as complex behaviour]
B37/S0245 N
[Has a 4c/25 glider: b5o$o4bo$o4bo$b5o!]
B3568/S136 N
B012345/S0246 N
B0134568/S0234 N
[The natural ship is actually an infinite class of ships]
B013457/S0123 G
[There are too many replicators]
B013458/S02 G
[There are too many replicators]
B01267/S0125 A
B358/S1267 N
B123478/S24678 S
[The negative rule is b3578s238, which is G, and have a replicator]
B01258/S025 G
[Possibly N]
B024678/S04678 S
[The negative rule is b3567s3578, which is G]
B0134568/S1234 S
[It has natural puffers, but not natural gliders]
B01238/S1246 G
B012/S015 F
B34/S368 F
B012357/S14678 S
[The negative rule is b3578s238, which is N]
B01234567/S035 A
B0123578/S135 A
B01246/S01234678 S
[The negative rule is b3s0135, which is both N and puffer-natural]
B346/S0567 G
B3468/S01 G
[Sometimes explodes]
B012458/S4 A
B0123457/S023678 S
[The negative rule of b347s02, which is G]
B012567/S014 A
[It converges to some strange states]
B348/S037 G
B123458/S024678 S
[Negative of b357s128, which is G]
B012/S145 A
B356/S034 G
[Maybe F]
B1578/S234678 S
[Negative of b378s24568, which is full of gliders]
B0123456/S01235 F
[Has a glider]
B01278/S012468 S
[Biphasic. May be regarded as complex behaviour]
B0138/S4 N
B0123578/S1236 G
[Heavy ameoba dynamics]
B3568/S0146 N
The region is determined by a neural network.
shouldsee wrote:Sure. It just took some cleaning work. I have updated the link on the frontpage. Although to apply for hexagonal, you would need to undertake a extensive change.
Undefined function or variable 'update_rule'.
Error in CA_console_opt2 (line 296)
update_rule
shouldsee wrote:The presence of fast decay rules is also very intriguing, since they are usually scattered on the other side of the distribution. One possibility is these F rules are closely related to some more interesting rules and thus inherited some characteristics.
F Rule Nearby N rule
B012/S015 B0125/S015
B34/S368 B34/S0368
B0123456/S01235 B012456/S01235
Bullet51 wrote:It seems that some files are missing in your package:
Bullet51 wrote:Dear Shouldsee,
I am puzzled by your definition of forward entropy and backward entropy. How are they different?
And what does the average of the 2-norm of [D_input' V_input(:,2)] mean? Why not just use the mean of the 2-norm of D_input' ?
dVV=[VV(1:3,:)-VV(4:6,:)];
wt=D_Tinput;
wt=wt/sum(wt);
v=[D_input' V_input(:,2)];
wtdVV=dVV(1:3,:).*repmat(wt,3,1);
v1=mean(dot(v,v,2)); %% this is obsolete
v2=mean(abs(wtdVV(1,:)));
v3=mean(abs(wtdVV(2,:)));
% v4=mean(wtdVV,2)'
%%these are actually recorded.
phaseX=v2;
phaseY=v3;
phaseZ=H_input;
;
outnumber=8; %% number of scalar outputs in the stat file
scalars={'phaseX','phaseY','phaseZ','H_input','HD_linput'}; %% varaibles recorded during souping---v1 and v are not recorded
shouldsee wrote:They are obsolete statistics that are no longer recorded in the 'process_outputs'.Code: Select alldVV=[VV(1:3,:)-VV(4:6,:)];
wt=D_Tinput;
wt=wt/sum(wt);
v=[D_input' V_input(:,2)];
wtdVV=dVV(1:3,:).*repmat(wt,3,1);
v1=mean(dot(v,v,2)); %% this is obsolete
v2=mean(abs(wtdVV(1,:)));
v3=mean(abs(wtdVV(2,:)));
% v4=mean(wtdVV,2)'
%%these are actually recorded.
phaseX=v2;
phaseY=v3;
phaseZ=H_input;
;
Bullet51 wrote:
I have figured out that H_input is the entropy of {NH now, NH 1 step before}, but what is the meaning of dVV?
HV=sum(VSD_Tinput,1)'; %% supposedly this should be forward entropy
HH=sum(HSD_Tinput,2); %% supposedly backward entropy
V_input=[HD_input' HV+HH HV-HH (1:18)']; %% combining into array
V=V_input(:,[2,3 ,1])'; %% reordering
VV=combvec(V,V); %% enumerate combination of points in the aforementioned 3d space
dVV=[VV(1:3,:)-VV(4:6,:)]; %% calulate vectors in 3d space, each corresponding to an NHT
wt=D_Tinput; %% read the number for each transition of NH (NHT)
wt=wt/sum(wt); %% normalise
wtdVV=dVV(1:3,:).*repmat(wt,3,1); %% weighting
v2=mean(abs(wtdVV(1,:)));
v3=mean(abs(wtdVV(2,:)));
shouldsee wrote:Code: Select all
HV=sum(VSD_Tinput,1)'; %% supposedly this should be forward entropy
HH=sum(HSD_Tinput,2); %% supposedly backward entropy
V_input=[HD_input' HV+HH HV-HH (1:18)']; %% combining into array
V=V_input(:,[2,3 ,1])'; %% reordering
VV=combvec(V,V); %% enumerate combination of points in the aforementioned 3d space
dVV=[VV(1:3,:)-VV(4:6,:)]; %% calulate vectors in 3d space, each corresponding to an NHT
wt=D_Tinput; %% read the number for each transition of NH (NHT)
wt=wt/sum(wt); %% normalise
wtdVV=dVV(1:3,:).*repmat(wt,3,1); %% weighting
v2=mean(abs(wtdVV(1,:)));
v3=mean(abs(wtdVV(2,:)));
Bullet51 wrote:Sure. It seems that the 4th column of V_input is never used.
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