manifest.json

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    },
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            "launchLabel": "Open the Pentagonal Lattice Geometry lab"
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            "id": "qqn",
            "title": "Quadratic Quasi-Newton",
            "pitch": "A new optimization algorithm for smooth functions that interpolates between gradient descent and L-BFGS.",
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            "subtitle": "Standalone · optimization"
        },
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            "title": "PID-Regulated Cellular Automaton",
            "pitch": "A cellular automaton whose update rule is a per-cell PID controller: each cell measures its active-neighbor count against a target and computes proportional, integral, and derivative terms to decide its next state. The result is a rule family with local memory (integral windup), local anticipation (derivative), and tunable dynamical regimes — under-damped ripples, critically-damped blobs, over-damped glassy creep — all from the same control-theoretic mechanism.",
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            "title": "Which Direction? → Where on the Curve?",
            "pitch": "An interactive, scroll-driven tutorial on the Quadratic Quasi-Newton (QQN) optimizer. Reframes optimization from \"which direction should I move?\" into \"where on this curve should I stop?\" — with live contour maps, deformable search curves, and a four-axis factoring that collapses a zoo of classical methods (gradient descent, momentum, L-BFGS, trust regions, OWL-QN) into points in one configuration space. <em>Built to make the geometry something you can feel, not just read.</em>",
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            "subtitle": "Interactive · optimization"
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            "id": "geometric-entropy",
            "title": "Geometric Entropy",
            "pitch": "A continuous analogue of the Erdős distinct-distance problem. Points on a manifold are arranged to extremize the Shannon entropy of their pairwise-distance distribution.",
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            "title": "RCC — Rational Certificate Complexity",
            "pitch": "The foundation of the trilogy. Treats every convergence sequence as a rational certificate engine, measures its bit-length versus demanded tolerance ε, and stratifies constants into cost classes (RC₁/RC₂/RC₃). Establishes the regularity condition, a Θ(log 1/ε) lower bound, and the central separation algebraic irrationals vs. π and e. <em>It fixes the vocabulary the other two essays invoke.</em>",
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            "subtitle": "Trilogy I · the foundational vocabulary"
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            "title": "Irrational Lattice",
            "pitch": "A new primitive: deterministic, algebraic “colored noise” for lattices. Coordinates in ℚ(√D) deform ℤᵈ and snap back via a nearest-lattice map — provably aperiodic, spectrally tunable, integer-arithmetic clean.",
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            "title": "PI_RCC — The Simplest Increment: x + sin(x)",
            "pitch": "A cubic-convergent iteration for π whose outer recurrence is <em>not</em> hypergeometric — it falls outside RCC's classified class, yet still attains optimal RC₁ cost. Develops derivative engineering and the tower of continua (ℚ → algebraic → analytic → elliptic/modular → periods). <em>Where RCC defines the cost classes, PI_RCC shows their boundary is permeable.</em>",
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            "subtitle": "Trilogy II · stress-testing the boundary"
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            "id": "nam",
            "title": "NAM — Numbers as Machines",
            "pitch": "A generator-based numerics library where every number is a forkable, deterministic nano-VM emitting an infinite digit stream. RCC's cost classes resurface here as generator state-dimension tiers, with a two-tier ABI, base-as-codec, BBP-as-resonance, and an honest interval account of equality. <em>Where RCC measures and PI_RCC engineers, NAM builds the machine that runs them all.</em>",
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            "icon": "NAM",
            "subtitle": "Trilogy III · the executable substrate"
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            "id": "spacelike-knots",
            "title": "Spacelike Knots",
            "pitch": "A knot equipped with a Minkowski metric, turning crossings into causal inversions. The distance matrix becomes a causal diagram: timelike, spacelike, and null separations color-coded across the whole knot.",
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            "id": "magnet-lattice",
            "title": "Magnet Lattice",
            "pitch": "Explore the dynamics of re-rotating magnets and their emergent behaviors.",
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            "id": "tel",
            "title": "The Extension Ladder: One Way to Watch Number Systems Grow",
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        },
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            "id": "text-block",
            "title": "Text Block",
            "pitch": "A tool for visualizing and interacting with sorted rotations of text strings.",
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            "id": "pastaponics",
            "title": "Pastaponics",
            "pitch": "A modular, 3D‑printed hydroponic medium enabling plant‑driven nutrient self‑regulation through spatially differentiated nutrient channels.",
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            "title": "Layered Cellular Automata",
            "pitch": "Langton's ants write a colored substrate that gates where Conway's Life is allowed to live. Three feedback layers — ants → substrate → life → substrate → ants — produce highways, colonies, and fractal boundaries. For a playable take on Conway's Life and 50+ other rulesets, see the sister site <a href=\"https://aol.cognotik.com/\" target=\"_blank\" rel=\"noopener\">The Arcade of Life ↗</a>.",
            "category": "lab",
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            "readme": "README.md",
            "video": "/videos/Binary_Coded_Layered_Autonoma.mp4",
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        {
            "id": "symmetry-simple",
            "title": "Space-Color Symmetry",
            "pitch": "A pixel canvas where symmetry doesn't just mirror your strokes — it rewires the diffusion graph. Heat flows along symmetry orbits, producing kaleidoscope dynamics on a quotient-like manifold.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "video": "/videos/Symmetry_Diffusion.mp4",
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        {
            "id": "experiments-basic",
            "title": "Basic Math Experiments",
            "description": "A set of interactive browser experiments: the Mandelbrot set, the Sieve of Eratosthenes, Fourier series epicycles, and the Collatz conjecture.",
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                "fractals",
                "primes",
                "fourier",
                "collatz",
                "canvas",
                "interactive",
                "visualization"
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            "href": "mandelbrot.html",
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            "author": "Fun With Math",
            "license": "MIT",
            "date": "2024-01-01",
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                "description": "Explore the Mandelbrot set, prime sieves, Fourier series and the Collatz conjecture in interactive, no-install browser demos.",
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                    "sieve of eratosthenes",
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                        "title": "Mandelbrot Set – Fun With Math",
                        "description": "Explore the Mandelbrot Set fractal interactively in your browser."
                    },
                    {
                        "href": "primes.html",
                        "title": "Prime Number Sieve – Fun With Math",
                        "description": "Watch the Sieve of Eratosthenes find primes interactively."
                    },
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                        "href": "fourier.html",
                        "title": "Fourier Series – Fun With Math",
                        "description": "Visualize Fourier series approximations with interactive spinning circles."
                    },
                    {
                        "href": "collatz.html",
                        "title": "Collatz Conjecture – Fun With Math",
                        "description": "Explore the Collatz Conjecture: the 3n+1 problem visualized."
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        {
            "id": "chaos-garden",
            "title": "Chaos Garden",
            "pitch": "An in-browser, gamified fluid dynamics simulation",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "video": "/videos/ns_flow_demo.mp4",
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            "icon": "CG"
        },
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            "id": "fractal-mosaic",
            "title": "Fractal Mosaic",
            "pitch": "A fractal mosaic provides infinite-zoom based exploration of your album.",
            "category": "lab",
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            "readme": "README.md",
            "video": "/videos/demo_mosaic.mp4",
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            "id": "gravity",
            "title": "Relativistic 2-Body Gravity",
            "pitch": "A 2-body gravitational system with relativistic adjustments and time-delayed (retarded) interactions. Gravity propagates at finite speed c, breaking Newton's third law and producing orbital precession, frame-dragging analogues, and chaotic orbits.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "video": "/videos/Relativistic_Gravity.mp4",
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            "section": "featured",
            "icon": "GR",
            "launchLabel": "Open the Relativistic 2-Body Gravity lab"
        },
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            "id": "markov-analysis",
            "title": "Bidirectional Markov Text Analyzer",
            "pitch": "Build a language model from your own corpus, then watch another text light up token-by-token by how <em>surprising</em> it is. Forward and backward order-n Markov models are merged into a single surprise heatmap, with click-to-replace predictions, add-k smoothing, backoff, and live perplexity.",
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            "icon": "MA",
            "launchLabel": "Open the Bidirectional Markov Text Analyzer lab"
        },
        {
            "id": "number-circuits",
            "title": "Number Circuits",
            "pitch": "What is the cheapest way to build a number using only 1s, addition and multiplication? Calculate, search and explore integer complexity.",
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            "readme": "README.md",
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            "section": "lab"
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        {
            "id": "mesh",
            "title": "Constrained Mesh Enclosure Lab",
            "pitch": "A deformable surface mesh flows downhill on geometric fitness functionals (area, volume, edge-length entropy, angular regularity, Laplacian smoothness) while an exact continuous collision-detection pipeline guarantees it never intrudes into an inner keep-out volume — a differentiable shrink-wrap where every gradient step is clipped at the moment of contact.",
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            "launchLabel": "Open the Constrained Mesh Enclosure Lab"
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            "id": "primegen",
            "title": "The Prime Sieve as a Stack of Orthogonal Periodic Fields",
            "pitch": "An interactive essay on the periodic machinery underneath the primes: each prime emits an orthogonal exclusion field, their stacked product has primorial period, and CRT independence makes density multiplicative, entropy additive, and spectral support disjoint.",
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            "launchLabel": "Open the Prime Sieve as a Stack of Orthogonal Periodic Fields lab"
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            "id": "static-secrets",
            "title": "Static Secrets",
            "pitch": "Publish encrypted content anywhere and decrypt it entirely in your browser. The host serves opaque bytes; only you hold the key.",
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            "id": "optimization-mechanics",
            "title": "Optimization Mechanics Visualizer",
            "pitch": "Drop GD, Adam, L-BFGS, and QQN onto the same rugged 2D loss landscape and watch, step by step, how each finds its way downhill. Configurable terrain (slopes, bowls, high-frequency noise, confounding lattices), a fading path with live gradient arrows, and projected statistics bars that expose the running gradient and squared-gradient accumulations adaptive optimizers quietly maintain. Step through QQN's oracle point, quadratic path, and line-search probes to see the mechanics papers describe in equations.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "order": 18,
            "repo": {
                "url": "https://github.com/Simiacryptus/optimization-mechanics.git",
                "branch": "main",
                "commit": "07292c78c2d49053c034cde8dcf95b54000cd07b",
                "path": "optimization/optimization-mechanics",
                "submodule": true
            },
            "dir": "optimization/optimization-mechanics",
            "source": "optimization/optimization-mechanics/entry.json",
            "section": "featured",
            "icon": "OM",
            "launchLabel": "Open the Optimization Mechanics Visualizer lab"
        },
        {
            "id": "nam-calculator",
            "title": "nam — Numbers as Machines",
            "pitch": "A calculator where every number is a deterministic, forkable virtual machine emitting an infinite digit stream on demand. Comparison is honestly tri-state, fork cost is annotated by tier, and unprovable digits render as 'pending (null)' rather than a comfortable lie.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "order": 19,
            "repo": {
                "url": "https://github.com/Simiacryptus/nam-calculator.git",
                "branch": "main",
                "commit": "6f76f3420ca80b037b09648a1ede0d03d8a3140d",
                "path": "numbers/nam-calculator",
                "submodule": true
            },
            "dir": "numbers/nam-calculator",
            "source": "numbers/nam-calculator/entry.json",
            "section": "featured",
            "icon": "NM",
            "launchLabel": "Open the nam interactive calculator"
        },
        {
            "id": "no3sieve",
            "title": "No-Three-in-Line: A Visual Theory Explorer",
            "pitch": "An infinite-canvas explorer for the no-three-in-line rule under deterministic greedy growth: ring-major Chebyshev order, forced empty strips, finite-horizon collinearity, density fields, top-K windows, and paranoid verification.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "order": 20,
            "repo": {
                "url": "https://github.com/Simiacryptus/no3sieve.git",
                "branch": "main",
                "commit": "3b101a172d3e99395ee0cb17e627693c262356ef",
                "path": "experiments/no3sieve",
                "submodule": true
            },
            "dir": "experiments/no3sieve",
            "source": "experiments/no3sieve/entry.json",
            "section": "featured",
            "icon": "N3",
            "launchLabel": "Open the No-Three-in-Line Visual Theory Explorer"
        },
        {
            "id": "3inline",
            "title": "No-Three-in-Line Explorer",
            "pitch": "An interactive laboratory for the classic no-three-in-line problem: place ~2n points on an n×n grid so no three are collinear along any rational slope. Solve it by hand with instant collinearity feedback, or watch an entropic simulated-annealing solver with parabola warm starts, sublattice mutations, and a tabu list search for dense configurations — all powered by an incremental line index for fast O(k) move checks.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "order": 21,
            "repo": {
                "url": "https://github.com/Simiacryptus/3inline.git",
                "branch": "main",
                "commit": "2fcf973e4bc049fa1e8ad6ab0eec0c08517ce4a8",
                "path": "experiments/3inline",
                "submodule": true
            },
            "dir": "experiments/3inline",
            "source": "experiments/3inline/entry.json",
            "section": "featured",
            "icon": "3L",
            "launchLabel": "Open the No-Three-in-Line Explorer lab"
        },
        {
            "id": "cutt",
            "title": "Coupled Uncertain Theory Trees",
            "description": "A new approach to decision tree learning that incorporates uncertainty and coupling between features.",
            "category": "labs",
            "href": "index.html",
            "readme": "README.md",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/cutt.git",
                "branch": "main",
                "commit": "f70a3f9bc9f1863e1c3d2d7796d2847282af5462",
                "path": "experiments/cutt",
                "submodule": true
            },
            "dir": "experiments/cutt",
            "source": "experiments/cutt/entry.json",
            "section": "labs"
        },
        {
            "id": "dihedral-attractors",
            "title": "Dihedral Attractors",
            "description": "Rung 4 of the geometric-energy ladder: sculpt meshes by optimizing functionals over triangulation dihedral angles — flatness, uniform folds, creasing, smoothness, or fold entropy — with points free or pinned to a sphere, torus, or saddle.",
            "tags": [
                "geometry",
                "discrete-differential-geometry",
                "dihedral-angles",
                "curvature",
                "triangulation",
                "optimization",
                "gradient-descent",
                "attractors",
                "polyhedra",
                "interactive",
                "visualization",
                "canvas"
            ],
            "category": "labs",
            "href": "index.html",
            "readme": "README.md",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/dihedral.git",
                "branch": "main",
                "commit": "4c1b84887983b1867768fa08d8cdcb857ebf07ed",
                "path": "experiments/dihedral",
                "submodule": true
            },
            "seo": {
                "title": "Dihedral Attractors — Sculpting Geometry by Optimizing Fold Angles",
                "description": "An interactive lab that minimizes or maximizes energies built from the dihedral angles of a live triangulation, coaxing point clouds into folded, curvature-defined attractors reminiscent of the Platonic solids.",
                "keywords": [
                    "dihedral angle optimization",
                    "discrete differential geometry",
                    "mesh curvature energy",
                    "geometric attractors",
                    "Thomson problem",
                    "gradient descent visualization"
                ]
            },
            "dir": "experiments/dihedral",
            "source": "experiments/dihedral/entry.json",
            "section": "labs"
        },
        {
            "id": "fractal-learning",
            "title": "Fitting Point Clouds with Iterated Transforms",
            "description": "An interactive TensorFlow.js lab that reverse-engineers an iterated function system from a target point cloud: a handful of affine transforms are enumerated to a fixed depth (commutative multisets via binary powers, or ordered words) and tuned by gradient descent against a symmetric Chamfer loss. Draw or load a target shape, pick the number of transforms and the depth, and watch a random constellation self-organize into the outline you asked for.",
            "tags": [
                "fractals",
                "iterated-function-systems",
                "ifs",
                "chamfer-distance",
                "gradient-descent",
                "autodiff",
                "tensorflow-js",
                "point-clouds",
                "optimization",
                "inverse-problems",
                "generative-art",
                "interactive"
            ],
            "category": "labs",
            "href": "index.html",
            "readme": "README.md",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/fractal-learning.git",
                "branch": "main",
                "commit": "eb8c81a712b542a61481214453e8f11a776aeb92",
                "path": "experiments/fractal_learning",
                "submodule": true
            },
            "seo": {
                "keywords": [
                    "iterated function system",
                    "IFS inverse problem",
                    "fractal compression",
                    "Barnsley fern",
                    "Chamfer loss",
                    "differentiable fractals",
                    "point cloud fitting",
                    "TensorFlow.js"
                ]
            },
            "dir": "experiments/fractal_learning",
            "source": "experiments/fractal_learning/entry.json",
            "section": "labs"
        },
        {
            "id": "opt-skeleton",
            "title": "Geometric Entropy Lab — No-Three-in-Line",
            "description": "A continuous relaxation of the no-three-in-line problem: line-centered potential wells with a non-monotonic population-fitness response f(p) = (p - 2)^2 attract points until a line holds two and repel once it holds three. Annealed Gaussian well width, a cosine lattice-snapping potential and TensorFlow.js optimizers (SGD / Adam / L-BFGS) crystallize points onto the n x n grid, with discrete integer verification of every configuration.",
            "tags": [
                "no-three-in-line",
                "combinatorial-geometry",
                "continuous-relaxation",
                "potential-wells",
                "gradient-descent",
                "annealing",
                "tensorflow-js",
                "visualization"
            ],
            "category": "labs",
            "href": "index.html",
            "readme": "idea.md",
            "author": "Wesley Roberts",
            "license": "MIT",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/opt-skeleton.git",
                "branch": "main",
                "commit": "26f4e0424531140c8300e1a42b72258b9b719658",
                "path": "experiments/opt_skeleton",
                "submodule": true
            },
            "seo": {
                "title": "Geometric Entropy Lab: Entropic Search for the No-Three-in-Line Problem",
                "description": "Interactive TensorFlow.js lab relaxing the no-three-in-line problem into a differentiable potential landscape, using population-fitness wells, annealed sigma schedules and lattice snapping to search for 2n-point grid configurations.",
                "keywords": [
                    "no three in line problem",
                    "population fitness response",
                    "continuous relaxation",
                    "lattice potential",
                    "entropic search",
                    "tensorflow.js optimization"
                ]
            },
            "dir": "experiments/opt_skeleton",
            "source": "experiments/opt_skeleton/entry.json",
            "section": "labs"
        },
        {
            "id": "gravitic-portals",
            "title": "Gravitic Portals",
            "description": "An interactive lab exploring the dynamics of gravitic portals and their effects on point clouds.",
            "tags": [],
            "category": "labs",
            "href": "index.html",
            "readme": "README.md",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/gravitic-portals.git",
                "branch": "main",
                "commit": "28f00cdedc6d800a63d6d815860e78416145a23c",
                "path": "experiments/gravitic-portals",
                "submodule": true
            },
            "dir": "experiments/gravitic-portals",
            "source": "experiments/gravitic-portals/entry.json",
            "section": "labs"
        },
        {
            "id": "camera-tool",
            "title": "Laser-Damage Camera Correction",
            "description": "An offline, installable PWA that profiles a camera sensor to find dead, stuck, hot and noisy pixels — including whole laser-burn patches — then infills the damage from healthy neighbours so a wounded sensor keeps taking clean photos. Everything runs on-device; no frame ever leaves the browser.",
            "tags": [
                "pwa",
                "camera",
                "image-processing",
                "computer-vision",
                "sensor-repair",
                "laser-damage",
                "offline",
                "javascript",
                "webrtc",
                "canvas"
            ],
            "category": "labs",
            "href": "index.html",
            "readme": "README.md",
            "author": "Nick Sullivan",
            "license": "MIT",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/camera-tool.git",
                "branch": "main",
                "commit": "62f6b385112b1a6e366ecdedaccbc0f6fc87b066",
                "path": "experiments/camera-tool",
                "submodule": true
            },
            "seo": {
                "title": "Laser-Damage Camera Correction — Profile and Repair a Damaged Sensor In-Browser",
                "description": "Profile your camera to map dead, stuck and hot pixels, then automatically infill the damage from healthy neighbours. A privacy-preserving, offline-capable PWA for laser-damaged and hot-pixel-afflicted sensors.",
                "keywords": [
                    "dead pixel repair",
                    "hot pixel correction",
                    "stuck pixel fix",
                    "laser damaged camera sensor",
                    "camera defect map",
                    "sensor calibration",
                    "dark frame analysis",
                    "pixel interpolation",
                    "progressive web app",
                    "client-side image processing"
                ]
            },
            "dir": "experiments/camera-tool",
            "source": "experiments/camera-tool/entry.json",
            "section": "labs"
        },
        {
            "id": "password-entropy",
            "title": "Password Entropy",
            "pitch": "A tool to calculate the entropy of a password.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/password-entropy.git",
                "branch": "main",
                "commit": "a8695e9f174279bcdc62a42c2a5ef66a267327c3",
                "path": "experiments/password-entropy",
                "submodule": true
            },
            "dir": "experiments/password-entropy",
            "source": "experiments/password-entropy/entry.json",
            "icon": "PE",
            "section": "lab"
        },
        {
            "id": "qqn-jax",
            "title": "QQN — Quadratic Quasi-Newton (JAX/Optax)",
            "description": "A pluggable JAX/Optax optimizer that blends steepest descent with a quasi-Newton oracle along a smooth quadratic path d(t) = t(1-t)(-∇f) + t²(-H∇f), letting a single line search pick the blend. No learning rate to tune. Factors optimization into four swappable axes — gradient, oracle, search, region — so L-BFGS, Newton, momentum, Barzilai-Borwein, Anderson, trust-region, OWL-QN and projected gradient all emerge as configurations.",
            "tags": [
                "optimization",
                "jax",
                "optax",
                "l-bfgs",
                "quasi-newton",
                "line-search",
                "trust-region",
                "machine-learning",
                "numerical-methods",
                "python"
            ],
            "category": "labs",
            "href": "spline_demo.html",
            "readme": "README.md",
            "license": "Apache-2.0",
            "order": 9007199254740991,
            "repo": {
                "commit": "f415c4a5dad43cf6b8af5ef52f926944fb8378d8",
                "path": "optimization/QQN/qqn-jax",
                "submodule": true
            },
            "seo": {
                "title": "QQN: Quadratic Quasi-Newton Optimizer for JAX",
                "description": "QQN interpolates gradient descent and L-BFGS along a quadratic path, discovering the right first-/second-order blend each iteration with no learning rate to tune. Pure-functional JAX: composes with jit, vmap, pmap and grad.",
                "keywords": [
                    "quadratic quasi-newton",
                    "QQN optimizer",
                    "JAX optimizer",
                    "optax",
                    "L-BFGS",
                    "line search",
                    "learning-rate-free optimization",
                    "cubic Hermite spline search",
                    "trust region",
                    "OWL-QN"
                ]
            },
            "dir": "optimization/QQN/qqn-jax",
            "source": "optimization/QQN/qqn-jax/entry.json",
            "section": "labs"
        },
        {
            "id": "slingshot-field",
            "title": "Slingshot Field",
            "pitch": "Gravitational slingshot effect in a rotating field.",
            "category": "lab",
            "href": "index.html",
            "readme": "README.md",
            "order": 9007199254740991,
            "repo": {
                "url": "https://github.com/Simiacryptus/slingshot-field.git",
                "branch": "main",
                "commit": "69d54fde8927d55903be65410fd214da941bd55c",
                "path": "experiments/slingshot-field",
                "submodule": true
            },
            "dir": "experiments/slingshot-field",
            "source": "experiments/slingshot-field/entry.json",
            "section": "featured",
            "icon": "SF"
        }
    ]
}