256 Tinker patches for 1-D elementary cellular automata rules

[syzygianrrf9999]

tinker_elementary_cellular_automaton_rules_algebraic_form.zip

Drive link, if the attachment doesn't work

With some scripting and a lot of research, I made 256 tinker patches representing these: https://atlas.wolfram.com/01/01/views/1 ... eView.html

That table is the algebraic forms for boolean equations that give the numbered binary sequence, if p, q, and r (or A, B, and C, on Tinker) are atomic boolean functions.

Translated from lifeless-nerd, this means, for example with oh, IDK, the patch for rule 69 (eca_auto69.repatch)...
...if we feed that Tinker 3 gate inputs on A, B, and C that have discrete rhythmic patterns equal to "11110000", "11001100", and "10101010", respectively (where 1=on/a pulse and 0=off/a rest)...
...the resulting rhythm pattern will be "01000101" (69 in binary).

The patches are of course named after these rules, but they only give those patterns with those specific inputs, but the logic/math they do naturally doesn't care what the inputs are, so think of them 256 unique rhythmic functions/fingerprints. If you alter the input patterns, their length, density, speed, etc, the resulting patterns will always change in a way that is unique to the patch. And of course you can feed them any CV; I'm sure these will do nutty things with LFOs.

Some simpler or perhaps rhythmically user-friendly patches (not exhaustive just pointing some more familiar/simple ones out) include:

3, 5, and 17: basic NOR gates
10, 34, 48, 68, 175, and 187: variants of implication gates (non-, converse-, etc., basically ANDs and/or ORs with one input inverted)
60 and 102: basic XOR gates
63: basic NAND gate
128: a three-input AND gate
202, 226, and 228: multiplexers/selectors that use A, B, or C respectively to toggle between the other two inputs.

More complicated ones that are famous for being seemingly endlessly complex, solving various computation problems and other fun stuff:

30: has no discernible pattern or mathematically known repetition
90: graphing its output gives pascal's triangle, modulo 2
110: Turing complete, kinda like Conway's Game of Life
184: solves for majority, only pulses if 2+ inputs are pulsing, regardless of which ones

(the above behaviors are theoretical for our purposes, since they would require the output to incrementally (i.e., on a linearly growing delay) be fed back to/replace the inputs cyclically, which doesn't really work in the context of CV (basically on any given beat, the output would need to be fed to A on the next beat, which would then have to cycle back to C on the beat after that, and so on). Still, the logic is there and they should still behave uniquely at for an extended duration (likely the LCM or something, of the inputs), and with inputs of varying/uneven length and asymmetrical rhythms, can approximate these behaviors to a finite degree).

Note that rhythmically, all these patches assume input pulses that are not sustained (i.e. each pulse consists of a 1-to-0/on-to-off progression; consecutive on-pulses are discrete rather than one long on-signal; 4 quarter note pulses rather than one sustained pulse over the same duration), and which share a common beat-division. I have no idea what these will do if you feed them dotted durations and/or triplets.

[Bes]

marry me

[syzygianrrf9999]

marry me

You don't want that, I'm high maintenance. Although I appreciate the implied praise

[selig]

marry me

You don't want that, I'm high maintenance. Although I appreciate the implied praise

I would give you high praise if I understood any of this.
To the point I was assuming from the thread title this was a bot spam post and had nothing to do with Reason/music. I was mistaken…
I DO understand the applications, just not how you got there!

Can you give any background to this concept, or gives some real world applications?

[syzygianrrf9999]

You don't want that, I'm high maintenance. Although I appreciate the implied praise

I would give you high praise if I understood any of this.
To the point I was assuming from the thread title this was a bot spam post and had nothing to do with Reason/music. I was mistaken…
I DO understand the applications, just not how you got there!

Can you give any background to this concept, or gives some real world applications?

Hoo boy. I'd be happy to try to. All of the concepts involved and arising from this stuff are still very much an area of research for me. One thing that will break the ice pretty fast is this: https://www.youtube.com/shorts/9Jua53-w4U4 - that is a video I only saw very recently but it is a concept that is all over my music. Basically every single number in binary can also be understood as an interval ratio (like 3:2, AKA a power chord/perfect 5th, AKA 10010 in binary, AKA 18 in decimal). Some of my absolute favorite REs of all time are Euclid, PSQ, and Tinker.

Some context for this obsession:
1. To put what I described above into practice rhythmically as well as tonally, given that most REs don't permit beat divisions smaller than 1/128, most songs I make are between 210 and 460 bpm, and I never use a sample rate smaller than 88.2k. I keep things like kicks and snares in half or even quarter time though, so 460 bpm sounds like an extremely energetic/anxious 115 bpm.
2. I hate making melody or tonality with keys and prefer making it in other ways, and I never learned to read sheet music or anything like that - guitar tabs probably ruined me for seeing letters as notes instead of numbers.
3. I've basically been using Reason and nothing else since version 2.5.
4. I hate using the sequencer and will do everything in the rack wherever possible.
5. I really enjoy recreational mathematics' relationship to music, which is hilarious because I was always a C/D math student.

As far as why anyone would use the patches here, like the elementary cellular automata rule 18 (to continue the earlier example) instead of just dialing in the pattern "10010" to a step sequencer, I like the idea that whatever inputs you fed that patch you could also feed individually to CV inputs elsewhere to make other instruments sort of "pseudo-harmonic" with that pattern, in a rhythmic sense. Again, still an area of research and experimentation for me. You can chain these patches together to create patterns of controlled chaos (another favorite concept - things that DO have a pattern, but which is difficult to discern in isolation, without say a 4/4 backbeat accenting it - another thing I enjoy doing).

Logic gates (which many of these patches are directly congruent with - our friend rule 18 can also be written as "(a XOR b XOR c) AND NOT b") I assume need no introduction as many REs include them, but not in a particularly extensive or self-chainable way without introducing a lot of CV delay, with Tinker being a somewhat notable exception. Chronologists' Truth and Robotic Bean's Elementary come to mind. But logic gates are also the building blocks for circuits and therefore a rudimentary form of programming. I find this (sending CV through logic gates to automate parameters) much more intuitive than drawing automation lanes in the sequencer, personally.

Any of this making sense? I'm gonna pause the book I'm writing here to check in lol. Do not let me fool you into thinking I'm an expert in any of this as I am constantly learning.

[selig]

5. I really enjoy recreational mathematics' relationship to music, which is hilarious because I was always a C/D math student.

You and I are 100% on the same page here, sucked at math in school but LOVE it now - it is pretty handy in RE design, for one example. I'm always looking for (and finding) special relationships between math and music.
Looks like I have a fun new rabbit hole to get lost in….

[joeyluck]

Looking forward to trying these out!

I was just using Tinker for the quadratic knob patch, which I really like to assign to filters. Assigning curves to knobs is something I miss inside the Combinator. I was tinkering about with the equation to try different curves, but I really don't know what I'm doing I should tinker more with Tinker

[selig]

Assigning curves to knobs is something I miss inside the Combinator.

I'll keep posting this 14 year old (and fairly crude) mockup every time someone mentions anything similar:

Screenshot 2025-01-10 at 2.10.30 PM.png