A map of (half of) all OTCA rules!
A map of (half of) all OTCA rules!
Purple  Spaceships are proven to not exist, also not explosive (heuristic)
Red  Spaceships are proven to not exist, also explosive (heuristic)
Blue  Spaceships are not disproved from existence, also explosive (heuristic)
Green  Spaceships are not disproved from existence, also not explosive (heuristic)
B0 rules are excluded (due to them having spaceships being hard to theorize about).
How the arrangements of rules works:
Take the X position of the pixel. (divided by 3, due to the upscaling)
Convert it to a 9 bit binary number (e.g 3 becomes 000000011)
Each bit now represents a birth transition (the first bit represents B0, 3 would be B78)
Do the same for the Y position to obtain your rule. For example, B3/S23 can be found at 32, 96 (or due to the upscaling, 96, 228)
The heuristic for whether a rule is explosive or not is not infallible. For example, you may notice a solitary purple dot in the large red area. This is the "fredkin replicator rule", or B1357/S1357. In this rule, every pattern is a replicator, however population experiences regular sharp drops, and the heuristic interprets this as the rule stabilizing (and thus it is not explosive).
Please let me know if you have any suggestions or questions!
Re: A map of (half of) all OTCA rules!
Code: Select all
x = 1, y = 1, rule = B1357/S1357
o!
So if Replicator (170, 170) is purple, then why not B1357/S02468 (170, 341)?
Code: Select all
x = 1, y = 1, rule = B1357/S02468
o!
Re: A map of (half of) all OTCA rules!
You could use the Gray code so that the rules for adjacent pixels only ever differ by one transition.
EDIT: If you wanted you could also order the bits of the Gray code so that the least significant bits (that change most often) represent the transitions that are least likely to affect the colour of a pixel. That way the rules of the same colour would tend to group together.
EDIT: If you wanted you could also order the bits of the Gray code so that the least significant bits (that change most often) represent the transitions that are least likely to affect the colour of a pixel. That way the rules of the same colour would tend to group together.
Re: A map of (half of) all OTCA rules!
I don't know the rules for extending the gray code, nor can I find them, though this would be very interesting!
Re: A map of (half of) all OTCA rules!
Have a look at the 'Converting to and from Gray code' section on that Wikipedia page. You actually only need the very simple BinaryToGray function they give there, which is just n^(n>>1) where ^ is XOR and >>1 is rightshift by 1 (I don't know what you're coding in, but Python would be the same as C). Then for each pixel (x,y), give it the colour that you would have given to (BinaryToGray(x),BinaryToGray(y)).
Re: A map of (half of) all OTCA rules!
I wrote a Processing program to rearrange the pixels of the original, and it looks like this:
Interestingly, everything is more "square". CGOL can be found at 144, 240 (yes, after the upscaling). Here it is shown in the outlined box. LaundryPizza03
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Re: A map of (half of) all OTCA rules!
How do I navigate this version of the map?Heavpoot wrote: ↑March 19th, 2020, 9:30 amI wrote a Processing program to rearrange the pixels of the original, and it looks like this:output.png
Interestingly, everything is more "square". CGOL can be found at 144, 240 (yes, after the upscaling). Here it is shown in the outlined box.Screenshot_20200319_132620.png
Code: Select all
x = 4, y = 3, rule = B3q4z5y/S234k5j
2b2o$b2o$2o!
The latest edition of newgliders.db.txt and oscillators.db.txt have 31117 spaceships and 1150 oscillators from outertotalistic rules. You are invited to help!
 LaundryPizza03
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Re: A map of (half of) all OTCA rules!
Just a few comments.
Spaceships are also known not to exist in rules with B23/S0, S123456, B34/S12345, B345/S1234, and S234567 without B2.
For rules with B0, see this post.
Spaceships are also known not to exist in rules with B23/S0, S123456, B34/S12345, B345/S1234, and S234567 without B2.
For rules with B0, see this post.
Code: Select all
x = 4, y = 3, rule = B3q4z5y/S234k5j
2b2o$b2o$2o!
The latest edition of newgliders.db.txt and oscillators.db.txt have 31117 spaceships and 1150 oscillators from outertotalistic rules. You are invited to help!
Re: A map of (half of) all OTCA rules!
Nice work!
A small suggestion: I've read from somewhere about a method that can differentiate Class 4 (potentially Turing complete) automata from other, more "trivial" ones, though I forgot where the original source was. Generate many pairs of random soups on a torus consisting of M cells, so that each pair of soups differ by only a single cell. Simulate the soups for a sufficiently long period of time, and observe how many cells differ in each pair of soups; we denote the latter number by N. Then for Class 1 automata (every pattern eventually die out), N=0; for Class 2 (only still lives and oscillators), N=O(1); for Class 3 (chaotic), N=O(M); and for Class 4, N obeys a continuous distribution from O(1) to O(M). Is it possible to classify the CAs using this method? This will yield information about the potential universality of the CAs, which I believe is more important than the presence or absence of spaceships or explosion.
A small suggestion: I've read from somewhere about a method that can differentiate Class 4 (potentially Turing complete) automata from other, more "trivial" ones, though I forgot where the original source was. Generate many pairs of random soups on a torus consisting of M cells, so that each pair of soups differ by only a single cell. Simulate the soups for a sufficiently long period of time, and observe how many cells differ in each pair of soups; we denote the latter number by N. Then for Class 1 automata (every pattern eventually die out), N=0; for Class 2 (only still lives and oscillators), N=O(1); for Class 3 (chaotic), N=O(M); and for Class 4, N obeys a continuous distribution from O(1) to O(M). Is it possible to classify the CAs using this method? This will yield information about the potential universality of the CAs, which I believe is more important than the presence or absence of spaceships or explosion.
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Re: A map of (half of) all OTCA rules!
Nice method! It is easy to make a script based on that.wzkchem5 wrote: ↑April 18th, 2020, 12:27 amNice work!
A small suggestion: I've read from somewhere about a method that can differentiate Class 4 (potentially Turing complete) automata from other, more "trivial" ones, though I forgot where the original source was. Generate many pairs of random soups on a torus consisting of M cells, so that each pair of soups differ by only a single cell. Simulate the soups for a sufficiently long period of time, and observe how many cells differ in each pair of soups; we denote the latter number by N. Then for Class 1 automata (every pattern eventually die out), N=0; for Class 2 (only still lives and oscillators), N=O(1); for Class 3 (chaotic), N=O(M); and for Class 4, N obeys a continuous distribution from O(1) to O(M). Is it possible to classify the CAs using this method? This will yield information about the potential universality of the CAs, which I believe is more important than the presence or absence of spaceships or explosion.
I have to disagree on the last statement, though. Most of the interesting rules won't show anything interesting after a random Ctrl5 soup.
Re: A map of (half of) all OTCA rules!
Yes, but the point is that the method can detect if the CA is Class 4 without needing to construct a universal computer, or even simply a reflector or something. The method just probes whether a small perturbation in the initial condition can generate either small scale, medium scale, or large scale changes in the final pattern. Class 1 and 2 automata do not allow for longrange communication, and you'll see N=O(1); Class 3 automata are so chaotic and experience the butterfly effect, that is even a small perturbation will generate a wholly different final outcome, and you'll see N=O(M). Only in Class 4 automata do you see information flows that can both easily transmit over long distances and easily be stopped, so that you have a broad distribution of N.
Of course, Class 4 phenomena does not imply universality, but as Stephan Wolfram famously pointed out, there is empirically a very strong correlation between the presence of Class 4 phenomena and universality. And that's what I mean by the "potential" universality of the CAs.
The Red Phoenix, The Yellow Phoenix, The Pink Phoenix And The Multicolored Phoenix
Re: A map of (half of) all OTCA rules!
Your method will classify Snowflakes, LeapLife, ATPP and Dominoplex as class 2.wzkchem5 wrote: ↑April 18th, 2020, 4:50 amYes, but the point is that the method can detect if the CA is Class 4 without needing to construct a universal computer, or even simply a reflector or something. The method just probes whether a small perturbation in the initial condition can generate either small scale, medium scale, or large scale changes in the final pattern. Class 1 and 2 automata do not allow for longrange communication, and you'll see N=O(1); Class 3 automata are so chaotic and experience the butterfly effect, that is even a small perturbation will generate a wholly different final outcome, and you'll see N=O(M). Only in Class 4 automata do you see information flows that can both easily transmit over long distances and easily be stopped, so that you have a broad distribution of N.
Of course, Class 4 phenomena does not imply universality, but as Stephan Wolfram famously pointed out, there is empirically a very strong correlation between the presence of Class 4 phenomena and universality. And that's what I mean by the "potential" universality of the CAs.
Re: A map of (half of) all OTCA rules!
Sorry but I'm not familiar with the names of these rules. I just learned about Snowflakes and found that it supports guns; therefore chances are that perturbing a single cell of a soup (that will not produce a gun otherwise) may produce a gun, and the gun can induce changes of N>O(1) cells. Did I miss anything?
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Re: A map of (half of) all OTCA rules!
The problem here is choosing the right scale. For example, Life is class 4 with practical soup sizes, but on extremely impractical scales (2^millions), it becomes class 3 due to the formation of junkclearing replicators and class3 metacells. The same thing happens with Snowflakes, which is normally class 2, eventually becomes class 4 (due to guns and stuff), and probably transitions into class 3 as well. There is also the possibility of a rule that appears to be class 4 but turns out to just be a really active class 2 rule.
Also, in my experience class4ish rules tend to be pretty boring and difficult to search (I used to look for them based on the idea that they would be interesting). What is more indicative of Turingcompleteness is the presence of small spaceships and multiple small highperiod oscillators. (Also, we don't actually know any ways for something to be universal without spaceships or signals)
Also, in my experience class4ish rules tend to be pretty boring and difficult to search (I used to look for them based on the idea that they would be interesting). What is more indicative of Turingcompleteness is the presence of small spaceships and multiple small highperiod oscillators. (Also, we don't actually know any ways for something to be universal without spaceships or signals)
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."
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Terry Pratchett
Re: A map of (half of) all OTCA rules!
P. S. Nonexplosive rules supports soupsearching, which is usually the most fruitful search method.

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Re: A map of (half of) all OTCA rules!
This is probably unreasonable, but is there a way to do this with nontotalistic rules?
also, bump
also, bump
woomy on a vroomy
Re: A map of (half of) all OTCA rules!
Hello, sorry, I keep forgetting to check the forums!
First of all, you need to convert the X and Y position to binary, from greycode (EDIT: downscale them first!). Then, just follow the instructions on the original post:
Well, technically, but you would need a 2251799813685248x2251799813685248 image (still excluding B0), and that seems very unreasonable (if memory serves, there are 51 survival and 51 birth conditions in INT rules!).googoIpIex wrote: ↑May 21st, 2020, 2:25 pmThis is probably unreasonable, but is there a way to do this with nontotalistic rules?
also, bump
Alright, thank you! I may post an updated version of this soonLaundryPizza03 wrote: ↑April 10th, 2020, 9:00 amJust a few comments.
Spaceships are also known not to exist in rules with B23/S0, S123456, B34/S12345, B345/S1234, and S234567 without B2.
For rules with B0, see this post.
Very late, sorry!
First of all, you need to convert the X and Y position to binary, from greycode (EDIT: downscale them first!). Then, just follow the instructions on the original post:
Heavpoot wrote: ↑March 18th, 2020, 8:20 pmTake the X position of the pixel. (divided by 3, due to the upscaling)
Convert it to a 9 bit binary number (e.g 3 becomes 000000011)
Each bit now represents a birth transition (the first bit represents B0, 3 would be B78)
Do the same for the Y position to obtain your rule. For example, B3/S23 can be found at 32, 96 (or due to the upscaling, 96, 228)
A map of all OTCA rules!
UPDATE:
Included more axioms, and all of the B0 axioms (thanks laundrypizza03!) which were very tedious to copy, so hopefully I didn't make any mistakes!
WITHOUT GRAYCODE: WITH GRAYCODE:
Included more axioms, and all of the B0 axioms (thanks laundrypizza03!) which were very tedious to copy, so hopefully I didn't make any mistakes!
WITHOUT GRAYCODE: WITH GRAYCODE: