GUZEN: the dice are a 48-bit number
A synthesizer whose six voices are decided by chance. A wavefolder adds the harmonics, a gate with memory shapes each note, and the dice turn out to be one 48-bit number.
Field notes on emergence, complexity & machines not from here
SpecimenGianni Pojani
Rule 137 is Rule 110 with black and white swapped: an automaton defined by eight bits that can compute anything computable.
Latest transmissions
7 received · decoding ongoing
Ptractable
ANTEVAULT: add, then multiply
A poker roguelite that runs in this tab. The best order for its scoring can be proved, its map can never trap you, and winning is a game against nature.
A memory leak has a shape
Most crashes on a hosting platform announce themselves minutes before they happen. This is how I taught one to read the warning, and when to let a machine act on it.
You need coherence
A language model can see every word of its context and still break the rules that context set. This post measures how fast that happens in a transformer and tests a small module that keeps the rate down.
Rule 137: eight bits that compute everything
The emblem of this site is a mirror image of Rule 110, and Rule 110 is a universal computer.
Gliders are messages
Five cells walk diagonally across the Game of Life. Build enough of them and you get a computer.
Hello, colony
First transmission. What this notebook is for, and how to read it.
The instruments
press ? anywhere for the manual
Atlas of the 256 elementary automataRunning an elementary automaton for n steps on n cells takes O(n²) time, and every property on its labels is checked by exhaustive or polynomial computation.PtractableGlider logicEvaluating a Boolean circuit is P-complete. This is the gate such circuits are built from.PtractableTamburo 8An eight-cell automaton has only 2⁸ states, so every evolving groove falls into a cycle that is found in polynomial time.PtractableOrfeo 32Fux’s rules only compare neighbouring notes, so the best counterpoint is a shortest path: O(n·k³) by dynamic programming. Everything else is a finite-state machine.PtractableMelencolia IA channel vocoder costs a fixed amount of work per band per sample, and the saddest four-chord phrase is a longest path in a layered chord graph, found by dynamic programming.PtractableGenomaEvery gene, loop and voice costs a fixed amount of work per sample, and a Euclidean rhythm of k pulses in n steps is laid out in O(n) time, as evenly as a straight line drawn on a grid.PtractableStochos 64One pattern holds 2^1024 gate configurations; searching them by brute force takes exponential time, which is why the generators exist.EXPexplosivePalinsestoIts spectral mask is Rule 110, which is Turing-complete: whether the mask ever settles into a repeating pattern is, in general, undecidable.REundecidableOfficinaPure Data and Orca are programming languages: whether a patch or a grid ever falls silent is the halting problem, undecidable in general.REundecidableTrappola 808A two-bar pattern is a finite table read in a loop: every step costs the same, and the whole thing runs in time linear in its length.PtractablePolvere 404Every pad press plays a buffer and every pattern is a finite list of hits read in a loop: each step takes a bounded amount of work.PtractableAutografoIts grid can run the Game of Life, which is Turing-complete: whether the text ever dies out, or settles, is undecidable in general.REundecidableFelceEach level of a fractal melody is the level above with every note replaced: a fixed amount of work for each note, so linear in the length of what is played.PtractableLanternaA feedback loop of image operators can run the Game of Life, which is Turing-complete: whether a network ever settles is undecidable.REundecidableCastelloEvery block of 48 samples is a fixed amount of work that must be done before the next one is due: a real-time machine is a polynomial-time machine with a deadline.PtractableCervelloWith mutation on, whether the machine ever plays a given bar again is a reachability question over its state space: the kind that lives in polynomial space.PSPACEstrategicAttrattoreWhether any progression satisfies a set of harmonic constraints is a constraint-satisfaction problem, NP-complete in general: easy to check, hard to find.NPverifiableNetwork of transmissions and ideasForce-directed layout converges in polynomial time per iteration; the graph itself is small and explicit.PtractableLabOn a bounded board, Life can simulate any polynomial-space Turing machine, so predicting its future is PSPACE-hard.PSPACEstrategicANTEVAULTA run is a few hundred moves long, so its best strategy is found by walking the game tree depth first: exponential time, polynomial space. Against a shuffled deck, that is a game against nature.PSPACEstrategicGUZENAll of its chance is one 48-bit random number generator, so a piece is a fixed function of its seed: constant work per sample, and the score can be found without rendering any audio.PtractableOrganismo 23There are 122 pins, and a patch is a way of putting them into groups. That is the Bell number B(122), about 6 × 10^148 patches, and some of them are feedback loops that can only be heard by running them.EXPexplosiveComplexity unveiledKolmogorov complexity is uncomputable. Only its upper bounds can be enumerated, which is exactly an RE property.REundecidable