Ideas, visualized started as an interactive companion to every numbered result in Walter Rudin’s three analysis books (1,062 theorems, lemmas, corollaries, propositions, and definitions) and expanded into a single directed acyclic graph of 6,684 ideas (6,621 interactive canvas simulations plus 6,890 planned syllabus nodes) across 85 collections and 13 fields. Every interactive figure below runs the atlas’s own zero-build canvas runtime (assets/js/viz/core.js, math.js, and its 17 domain kits) directly on the compiled graph.

Zero build in the browser, one pass on disk

Each chapter is a plain ES module under content/<col>/. scripts/build.mjs resolves the global dependency DAG and writes static JSON shards; the browser imports chapter modules directly with no bundler.

Adding a collection requires only a folder with a collection.js descriptor and chapter modules exporting statement, idea, deps, and viz(v). On build, scripts/build.mjs verifies that all 11,541 dependency edges form a cycle-free DAG, computes each item’s transitive ancestor and descendant closures, packs chapters into 88 shelf rows using eight forward-and-backward barycentre sweeps, and derives light and dark collection hues in perceptual OKLCH space.

6,684 ideas in one dependency graph

All 6,684 written ideas and 11,541 dependency edges across 85 collections and 13 fields. Click or dragTap or drag on the atlas to pan and zoom, select any node to light up its full transitive prerequisite and descendant cones, switch to the 13-field chord matrix, or scrub the 77-step longest reasoning chain.

Because deps cross chapter, book, and discipline boundaries, a single click traces how foundational definitions propagate across the entire graph: an order on a set (pma-1.5) sits at depth 0 with 3,286 downstream descendants; uniform continuity on compact sets (pma-4.19) bridges metric topology into integration and Fourier analysis; the real spectral theorem (ladr-7.29) feeds 664 results across mechanics, quantum theory, and statistics; the 1,989 cross-field links carry mathematical structure into physics (446), engineering (116), statistics (110), computer science (104), and economics (93); and the 77-step longest chain runs unbroken from pma-1.5 through complex and functional analysis, wave mechanics, and quantum gates to Grover’s search algorithm (cplx-13.9).

Thirteen fields, one canvas runtime

Thirteen live simulations—one from each field—mounted directly by assets/js/viz/core.js. Switch fields, drag handles and sliders on the canvas, flip hypotheses, or open the viz(v) source drawer to see the declarative stage calls behind each picture.

Every simulation in the repository is written against the same 3,531-line runtime (core.js + math.js) and 17 domain kits. Instead of static diagrams, each viz(v) exposes the quantity the proof or mechanism controls: you can break compactness on (0, 1] in pma-4.19 and watch the greatest admissible δ(p) collapse to zero near the missing endpoint, drag the launch velocity in mech-8.22 as Keplerian velocities trace an exact circle in hodograph space, drag Greenland to the equator in geog-4.4 to shed its 14× sec²φ Mercator inflation, reconstruct a CT phantom from its Radon sinogram in imaging-3.3, tip an integrated city into segregation in soc-1.2, or snap one tooth off the Antikythera b1 gear in tech-2.9 and watch the Metonic pointer drift.

One mathematical spine, many disguises

Eight cross-field bridges (104 steps) and 450 landmark papers (350 BCE – 2020 CE) across the 13 field lanes. Select a bridge and click any step along its track to run that step's interactive simulation live below the swimlane.

The same mathematical skeleton repeatedly reappears under different physical or social names. Following the spectral theorem bridge walks from self-adjoint matrices (ladr-7.29) and SVD (ladr-7.70) to coupled normal modes (mech-11.4) and standing waves on a string (music-2.3); the entropy bridge links Boltzmann microstates (thermo-5.6) to Shannon information (info-1.2) and Landauer’s k_BT ln 2 erasure bound (thermo-5.17); the fixed-point bridge connects Banach contraction (pma-9.23) to Nash equilibria (game-2.3) and PageRank (stoch-4.15); and switching to the 450 landmark papers plots each primary source on the field timeline alongside the graph nodes it introduced.

Auditing 6,621 canvases without eyes

Coverage across all 85 collections and live numerical audits from scripts/check.mjs and the 161 tests/verification-*.test.mjs suites (1,058 tests, 6,906 assertions).

Keeping 6,621 interactive canvases honest requires automated checks at two levels. In headless Chromium, scripts/check.mjs --modes mounts every item in tools/harness.html, clicks through every segmented control and toggle, verifies that every visible canvas paints non-transparent pixels, and flags raw-string TeX backslash escapes or missing live readouts. In Node, 161 primary-source verification suites test the underlying solvers against independent quadrature and published datasets—catching discarded negative-k_x imaginary residuals and sub-Nyquist detector aliasing in Fourier CT (imaging-3.4), separating exact discrete log-odds selection ln(1 + s) from the weak-selection s approximation (popgen-4.2), and auditing every control mode and primitive family across the 85 collections.