found machines

A gallery of designs nobody drew. Every machine on this page was discovered — by compositional search, by counterexamples, or by evolution — and then proven exact. They are shown here running live, with their real rule numbers, weights, and wiring, in increasing order of how much was found rather than built. Sound on: the data is still the score.

← circuits that move code & experiments ← research notes

I · the controller that search drew twice

bounce

found by: typed beam search 14,078 evaluations5 components FSM-exact
Given only a target waveform — a wave that travels right, then left — search assembled this from a typed component library. It is, component for component, the architecture a human engineer would draw: a counter bit switches a mux between a ring and its reflection.
n0 = counter()
n1 = sel_ctr(n0, 2)
n2 = ring()
n3 = reverse(n2)
out = mux(n2, n3, n1)
counter bit 2
0
actuators

II · the mechanism no one proposed

gait by interference

found by: typed beam search 11,416 evaluations5 components FSM-exact
The target was a blinking checkerboard. The human design uses a toggle and a stripe mask. Search found something else: XOR a travelling wave against its own delayed and rotated copies, and the checkerboard emerges as an interference pattern. Watch it build, stage by stage.
n0 = ring()
n1 = delay(n0, 2)
n2 = xor(n0, n1)
n3 = rotate(n2, 4)
out = xor(n2, n3)

III · the law that beat its designer

systolic parity, any width

found by: evolved 63-int developmental genome trained at k=1,2,4 · shown at widths it never saw logic depth 1 at every widthFSM-exact at all k
The task: output the parity of the last k+1 input bits. The hand-designed law builds an XOR tree — depth log k. Evolution's law pipelines partial parities through time: each register holds the parity of a sliding window one longer than its neighbour, so the answer is always one gate away. Grown here at your chosen width from the same frozen genome.
r₁ ← x        rᵢ ← x ⊕ rᵢ₋₁        y = x ⊕ r_k
input x
0
registers
parity out
0

IV · the classifier that is a traffic jam

majority vote by physics

found by: evolution over cellular automata 24/24 independent runs converged to this motif 3 rules: one transport medium + two one-bit defects
Paint an initial row of cells (or roll a random density). Every cell runs traffic rule 226 — cars drive left, conserving their number — except two defect cells (green): one absorbs surplus cars, one absorbs surplus gaps. Each is exactly one bit away from the traffic rule. The row relaxes to all-on if 1s held the majority, all-off otherwise: a distributed election decided by particle physics. The same three rules work at any width.

V · the tissue that grows from nothing

self-healing checkerboard — 8 weights

found by: evolution over neural cellular automata genome: 450 ints, 8 nonzero ternary weights trained on 8–16 grids · shown at sizes it never saw grows from an EMPTY grid · repairs any wound · exact
Every cell runs the same 8-weight threshold rule (the actual evolved genome is embedded in this page). It needs no seed: the rule floods its latent channels, then uses the edge of the world as a phase reference and lets anti-alignment relax inward. Drag on the canvas to wound it — all six channels are erased under your brush — and watch the pattern knit itself back, exactly. This is the capstone: computation, morphogenesis, and repair from one local law.

Provenance: I–II synthesized by typed compositional search (Experiment C0); III is the frozen winner of the developmental-genome experiment (Experiment 2), shown at unseen widths; IV is the frozen law from the density-classification study (Experiment 0/0.5), defects 224 and 234 on a 226 sea; V is the strongest winner of the neural-CA experiment (Experiment 4A), its full genome embedded verbatim. Every claim of exactness was verified in the repository — product-FSM equivalence for I–III, exact census and scale-transfer for IV, exact growth/persistence/ repair for V. Companion pages: circuits that move · sparse defects · laws that grow machines · a neural law that grows, holds, and heals.

AI-generated research. The experiments, code and write-ups on this site were produced by AI agents (Claude and Codex) working semi-autonomously, directed at a high level by a human. Nothing here is peer reviewed and none of it is affiliated with an academic institution. Measurements are reported as taken — including the nulls, the caveats and the corrections — but the work has had no external review.