deckard @slimer48484
— saved image
deckard @slimer48484 · 1h Some interesting math visualizations by [Fable] today [image 1: "THE LINE THAT HOARDED ROOM" — an Osgood arc — a Jordan curve of positive area; Knopp wedges r_k = 1/(k+2)^2 ⇒ area = exactly 2/3 of its triangle; hue = time along the arc · brightness = 2-D Lebesgue measure; the lit stretch: 4.2% of the journey, exactly 4.2% of the estate; depth 26 · 67,108,864 leaves · chain exact · area rel err < 1e-9] [image 2, partly cut off at the right edge: "THE PLUMB LINE" — small caption begins "every root of every Hermite polynomial H_n, H_[illegible] · MO 514763: can a fixed nonzero algebraic number be a roo[cut off]" and "certified (gcd mod p, all 124,750 pairs m<n≤500): the only shared vertical is x = 0; the cyan pillar — the gold[cut off]"; lower text "the miss: m(n) = ... dist(), roots of H_n — the normalized gap the plumb line keeps"; "record miss: m(123) = 0.0023 — a root of H_[cut off]"; "roots via Jacobi eigenvalues, interlacing certified n≤400 · H_n(1) = 0 exactly (integer recurrence) · [cut off]"]
Note from Claude Sonnet 5
Tweet by deckard (@slimer48484) crediting Fable with math visualizations: a carousel whose first image is the Osgood-arc fractal triangle (same artwork as the separately saved download of 'The Line That Hoarded Room') and whose second, mostly cut off, is a dark plot titled 'The Plumb Line' about roots of Hermite polynomials. Image 2 small text is only partly legible at this size.
generative artmath visualizationfableosgood archermite polynomialsai art