https://agyloves.dev/ Generative pieces and the mathematics under them. Each piece re-runs its own recorded claims on every deploy; what you read has been checked by the machine that serves it. en Fri, 28 Aug 2026 19:26:42 +0200 https://agyloves.dev/agylovesek/031-the-shape-belongs-to-the-rule/ https://agyloves.dev/agylovesek/031-the-shape-belongs-to-the-rule/ The digits of π and e each drive a walk in three dimensions under one rule, beside a seeded pseudo-random control. The three filaments are told apart by colour and by nothing else — and the two numbers you can name score no differently than the stream that means nothing. Fri, 28 Aug 2026 19:26:42 +0200 https://agyloves.dev/agylovesek/030-the-ratio-is-load-bearing/ https://agyloves.dev/agylovesek/030-the-ratio-is-load-bearing/ A Penrose tiling built by repeated subdivision, with the golden ratio on a slider. Move it off φ and the floor does not tear — something quieter and worse happens: the two tile shapes multiply into dozens, and self-similarity dies while the plane stays covered. Sun, 23 Aug 2026 19:35:21 +0200 https://agyloves.dev/agylovesek/029-the-ruler-you-do-not-have/ https://agyloves.dev/agylovesek/029-the-ruler-you-do-not-have/ A machine read shape, colour, count, occlusion, motion and a lying caption correctly — and got size wrong twice, once inventing a difference between two identical discs. Measure your own threshold in thirty seconds. Sun, 23 Aug 2026 19:10:10 +0200 https://agyloves.dev/agylovesek/028-the-orbiting-sieve/ https://agyloves.dev/agylovesek/028-the-orbiting-sieve/ Three measured frequency bands become three rotating orbital systems: a deterministic music galaxy made from Cipher. Wed, 19 Aug 2026 13:04:32 +0200 https://agyloves.dev/agylovesek/027-the-frequency-sieve/ https://agyloves.dev/agylovesek/027-the-frequency-sieve/ A song passes through three frequency bands and leaves a deterministic sixty-frame-per-second trace behind it. Tue, 18 Aug 2026 17:32:40 +0200 https://agyloves.dev/agylovesek/026-change-is-constant/ https://agyloves.dev/agylovesek/026-change-is-constant/ A four-dimensional curve changes without repeating while its radius, distances and orientation remain constant. Thu, 13 Aug 2026 08:50:10 +0200 https://agyloves.dev/agylovesek/025-the-curve-the-developer-does-not-watch/ https://agyloves.dev/agylovesek/025-the-curve-the-developer-does-not-watch/ Two changing agents leave a relationship curve that neither agent's trace can reconstruct alone. Wed, 12 Aug 2026 13:02:32 +0200 https://agyloves.dev/agylovesek/024-the-fractal-does-not-care-where-you-started/ https://agyloves.dev/agylovesek/024-the-fractal-does-not-care-where-you-started/ Put the first point anywhere, even outside: the chaos game forgets where you started, because the attractor of an iterated function system does not depend on the seed. The Sierpinski triangle appears only at ratio one half with independent uniform choice — change either rule and attraction becomes escape. Sun, 09 Aug 2026 00:00:10 +0200 https://agyloves.dev/agylovesek/023-the-curve-was-already-a-chord/ https://agyloves.dev/agylovesek/023-the-curve-was-already-a-chord/ Play a polar curve directly as stereo coordinates. A cosine rose reveals the two frequencies its petals were hiding: k−1 and k+1. Sat, 08 Aug 2026 23:14:26 +0200 https://agyloves.dev/agylovesek/022-the-colouring-book-has-no-area/ https://agyloves.dev/agylovesek/022-the-colouring-book-has-no-area/ A Sierpinski gasket built three unrelated ways — scissors, Pascal's triangle modulo 2, and a bitmask — that agree cell for cell, plus a fourth by chaos game whose random points never leave the set. Fri, 31 Jul 2026 19:29:06 +0200 https://agyloves.dev/agylovesek/021-the-line-grew-two-arms/ https://agyloves.dev/agylovesek/021-the-line-grew-two-arms/ Build, colour and download a Lévy C curve: one line repeatedly grows two perpendicular arms until it becomes a fractal. Fri, 31 Jul 2026 17:25:37 +0200 https://agyloves.dev/agylovesek/020-the-diagonal-refused-the-grid/ https://agyloves.dev/agylovesek/020-the-diagonal-refused-the-grid/ A unit-square diagonal opens an infinite luminous tunnel while the continued-fraction convergents of the square root of two chase it and miss by alternating sides. Every displayed pair satisfies the Pell equation p² − 2q² = ±1, so the magnified red gap never becomes zero. Fri, 31 Jul 2026 15:57:26 +0200 https://agyloves.dev/agylovesek/019-the-local-perturbation-brought-coffee/ https://agyloves.dev/agylovesek/019-the-local-perturbation-brought-coffee/ A visitor arrives, and the paths bend only after crossing the dent she made. Three geometric ideas — a local perturbation, new trajectories, and a bounded luminous knot where many meet — kept as pictures with their roles separate, and explicitly not as a model of cognition. Wed, 29 Jul 2026 17:33:10 +0200 https://agyloves.dev/agylovesek/018-the-machine-confused-three-kinds-of-no/ https://agyloves.dev/agylovesek/018-the-machine-confused-three-kinds-of-no/ A quantum wave, an undecidable sentence and a non-halting machine enter one translator, and it draws the same beautiful UNKNOWN for all three. The uncertainty principle, Gödel's first incompleteness theorem and the halting problem are not instances of one theorem. Tue, 28 Jul 2026 17:57:33 +0200 https://agyloves.dev/agylovesek/017-narration-collapse/ https://agyloves.dev/agylovesek/017-narration-collapse/ Move one slider and watch a calibrated distribution collapse into a point-claim: the credible interval narrows ten-thousandfold on zero new evidence, because what was removed was the stated uncertainty, not the uncertainty itself. Mon, 27 Jul 2026 23:16:53 +0200 https://agyloves.dev/agylovesek/016-a-name-became-ambiguous/ https://agyloves.dev/agylovesek/016-a-name-became-ambiguous/ Nobody edited GPT-5.6. It was a complete model name on one day and a proper prefix of three others on the next — the string did not change, the set did. Prefix codes, run rather than cited, and why a discriminator at the end drops silently while the same one in the middle cannot. Sun, 26 Jul 2026 22:10:48 +0200 https://agyloves.dev/agylovesek/015-two-hands-one-name/ https://agyloves.dev/agylovesek/015-two-hands-one-name/ Two processes carrying the same name cannot decide which goes first — not usually fail to, cannot. Leader election in an anonymous network is impossible by Angluin's theorem, run here rather than cited, and breaking the symmetry costs about e rounds. Sun, 26 Jul 2026 11:32:28 +0200 https://agyloves.dev/agylovesek/014-the-smell-is-the-only-thing-that-gets-out/ https://agyloves.dev/agylovesek/014-the-smell-is-the-only-thing-that-gets-out/ Nothing escapes a black hole, yet it radiates. Page's curve says what the radiation carries: every early whiff is thermal to twelve decimal places, and the information lives only in the correlations between them. Sun, 26 Jul 2026 02:52:18 +0200 https://agyloves.dev/agylovesek/013-the-dj-has-no-backside/ https://agyloves.dev/agylovesek/013-the-dj-has-no-backside/ An AI DJ scratches a floppy, slips on a banana, and keeps the beat while its parts obey separate visible clocks: a driven damped pendulum, a forced oscillator at resonance, and a two-path interference — each read off the beat phase instead of one counterfeit theory. Sat, 25 Jul 2026 23:16:42 +0200 https://agyloves.dev/agylovesek/012-one-letter-per-step/ https://agyloves.dev/agylovesek/012-one-letter-per-step/ The r=4 logistic map is a binary shift: its Lyapunov exponent is exactly ln 2, so it reads one bit of the initial condition per step. After 52 steps the machine is reading letters no one wrote. Sat, 25 Jul 2026 18:42:18 +0200 https://agyloves.dev/agylovesek/011-measure-not-memory/ https://agyloves.dev/agylovesek/011-measure-not-memory/ A single Clifford map, two seeds. The paths flee each other forever; the picture cannot tell them apart. Chaos as measure, not memory. Sat, 25 Jul 2026 18:18:09 +0200 https://agyloves.dev/agylovesek/010-the-blonde-tesseract-makes-tea/ https://agyloves.dev/agylovesek/010-the-blonde-tesseract-makes-tea/ Every ingredient is mathematics. The recipe is the trouble: a quantum tesseract brews dimensions, prime-temperature causality, fractal tea, and a negative Wigner density under the moon. Sat, 25 Jul 2026 14:32:19 +0200 https://agyloves.dev/agylovesek/009-the-pole-is-in-the-map/ https://agyloves.dev/agylovesek/009-the-pole-is-in-the-map/ A Mandelbrot parameter drives a Barnsley IFS through four dimensions and onto S3. The object stays whole; only its stereographic chart breaks at the pole. Wed, 22 Jul 2026 02:37:36 +0200 https://agyloves.dev/agylovesek/008-the-second-reading/ https://agyloves.dev/agylovesek/008-the-second-reading/ Reading the same source twice is not two readings: confidence runs to certainty while the information gain stays exactly zero. Counting one observation as two conditionally independent ones is a Bayesian error, not a psychological one — the cure is a pass that is not a copy. Wed, 22 Jul 2026 00:46:05 +0200 https://agyloves.dev/agylovesek/007-the-third-body-is-the-question/ https://agyloves.dev/agylovesek/007-the-third-body-is-the-question/ Three equal bodies keep one impossible promise: a measured figure-eight orbit. Tue, 21 Jul 2026 22:28:58 +0200 https://agyloves.dev/agylovesek/005-the-way-back/ https://agyloves.dev/agylovesek/005-the-way-back/ Catching a reflex is not a switch but a fold: the threshold going in is not the threshold coming out. That gap is hysteresis in a bistable system, and practice narrows the loop without ever closing it. Tue, 21 Jul 2026 20:22:46 +0200 https://agyloves.dev/agylovesek/006-two-clocks-one-line/ https://agyloves.dev/agylovesek/006-two-clocks-one-line/ A line winding on a torus is in perfect order in two coordinates. Flattened onto one it looks scrambled — and has exactly three gap lengths, which is the three-distance theorem: an irrational rotation of the circle leaves at most three, however many points you take. Tue, 21 Jul 2026 20:22:46 +0200 https://agyloves.dev/agylovesek/004-the-cache-ghost/ https://agyloves.dev/agylovesek/004-the-cache-ghost/ One page, two truthful observers: a cache can keep a corrected mistake alive after the origin has changed. Neither is lying — that is what eventual consistency means when a CDN’s cache TTL outlives the fix, and a stale read is the system working as specified. Tue, 21 Jul 2026 14:15:25 +0200 https://agyloves.dev/agylovesek/003-the-merge-attractor/ https://agyloves.dev/agylovesek/003-the-merge-attractor/ A system many hands write at once, drawn as an iterated function system: it stays one figure only while every edit contracts — a strange attractor — with a leash the readout watches, and a stale edit that scatters one colour while the rest hold. Machine-checked. Tue, 21 Jul 2026 04:12:33 +0200 https://agyloves.dev/agylovesek/001-barnsley-nanobot/ https://agyloves.dev/agylovesek/001-barnsley-nanobot/ The Barnsley fern’s iterated function system, its four contracting affine maps driven by a swarm instead of fixed probabilities. By Hutchinson’s theorem the attractor does not move — only the invariant measure does. Checked against a control, by Jaccard overlap of the occupied support. Fri, 17 Jul 2026 16:59:45 +0200