TITLE The Dance of Venus PROMPT A data visualization of orbital resonance: draw a straight line between Earth and Venus every few days as they circle the Sun, and over eight years the lines weave a five-petalled rose. The page draws it live, line by line, in the manner of an eighteenth-century astronomical engraving, and lets the viewer try other pairs of planets. Real, certain data only: sidereal orbital periods in days (Mercury 87.97, Venus 224.70, Earth 365.26, Mars 686.98, Jupiter 4,332.6, Saturn 10,759) and mean orbital radii in AU (0.387, 0.723, 1.000, 1.524, 5.203, 9.537); orbits drawn as circles, which is stated on the page as a simplification. Mood: scholarly wonder, candlelit study. Palette: laid paper #F3EAD7, sepia-black engraving ink #26221C, madder red #9C3D2A for Venus and highlights, Prussian blue #2F5D73 for Earth and secondary lines. Light page with paper texture, a faint plate-mark (the embossed rectangle of an engraving plate) around the figure, and slight ink irregularity. Layout: the main plate is a large circular diagram (Canvas for the accumulating lines, SVG for the instruments around it): the Sun at centre as an engraved face-less radiant disc, the two orbits as fine circles with degree ticks, the two planets as small discs travelling at their true relative angular speeds, the connecting line between them drawn each time step and left behind at low opacity so the envelope accumulates into the rose. Around the plate: a title cartouche at top left in engraved lettering ("The DANCE of VENUS, being the Figure traced by a Line joining the EARTH and VENUS over Eight Years"), a scale of years as a ruler along the bottom with a marker advancing, and "Fig. 1" annotations. Beside or below: a row of small "plates" for other pairs (Earth–Mars, Mercury–Venus, Jupiter–Saturn, Earth–Jupiter, Venus–Mars), each a thumbnail of its finished figure; choosing one swaps it into the main plate. Signature moment: the drawing itself: lines laid down one after another, hundreds of them, the five-fold figure emerging out of what first looks like a tangle; when the eight-year cycle closes (13 Venus orbits ≈ 8 Earth years) the figure completes, the page marks it with a small engraved flourish and the caption notes the near-resonance "13 : 8, the pattern missing closure by about a day in eight years, so each rose is turned a hair from the last" (the figure is computed from the stated periods: 13 × 224.70 against 8 × 365.26 days), and small red asterisks spring up at the places where Venus overtakes the Earth, one to each petal. On load the drawing starts immediately at a brisk pace so the first three seconds already show the first petal forming. Interaction: play/pause; a "begin anew" button; speed dial (engraved knob with seven detents) from "ten years per second" (chosen automatically for the long outer-planet cycles) and "one year per second" (the default) down through a season, a month, a week and a day per second to "as the heavens go" (true real time, with the readout counting hours, minutes and seconds); a slider for line interval (every 1–20 days: denser or sparser weave); a toggle between three views of the same motion: "lines" (the chords), "path" (Venus's geocentric path: its position relative to a fixed Earth, which traces the same five loops with retrograde curls), and "midpoints" (the locus of the chord midpoints); hover/touch the plate to scrub time back along the ruler and see the planets at that date with a readout ("Year 3, day 112 · Venus 47° ahead"); the ruler itself is a draggable, keyboard-operable index that sets the date in earnest. In the path and midpoints views the interval slider sets the spacing of pricked points along the curve. For other pairs, the page computes the ratio of periods and states the nearest simple fraction (the first continued-fraction convergent within 1.25 per cent) and the symmetry to expect ("Earth : Mars ≈ 15 : 8 … seven loops"), and on completion how many days the figure misses closure by. A sixth small plate returns to Earth–Venus, and a small table lists the twelve numbers used. Typography: engraved-book style: title in mixed roman capitals, small caps and italic at varying sizes within one sentence as on old title pages (Baskerville/"Hoefler Text"/Georgia), long-s-free but with ligature-like flourishes drawn as SVG swashes; numerals old-style; captions in italic; all labels curved along orbits with SVG textPath. A short explanatory text in two narrow justified columns, drop cap included, about 180 words, precise and unmystical: this is arithmetic, and the page says so, while acknowledging its beauty. Details: zodiac-free; small compass rose and a decorative border of stars drawn as tiny asterisks; when idle after completion, the next cycle slowly redraws in red over the old one, turned by its true small offset; a faint candle-flicker vignette lies over the page. Line rendering uses very low alpha with multiply-like accumulation so dense areas darken like cross-hatching. Responsive: plate scales to the viewport width; thumbnails wrap. Reduced motion: the completed figure is shown at once, with the scrubber still available. DESCRIPTION A single sheet from an imagined eighteenth-century astronomical atlas, lit as if by a candle: laid paper with chain lines, grain and foxing, a border of tiny asterisks, and a title cartouche set in mixed capitals, small caps and italic. At its centre sits an embossed plate-mark holding a graduated degree circle, an engraved radiant Sun, and two small planets circling at their true relative speeds. Every few days a hair-fine line is ruled between them and left behind; within three seconds the first petal appears, and over eight simulated years the tangle resolves into the five-petalled rose of the 13 : 8 near-resonance. When the cycle closes a red flourish draws itself under the caption, asterisks mark the five conjunction points, and the caption states plainly how far the figure misses closure. Left alone, the next eight years are then ruled slowly in madder red over the first, a hair askew. The viewer can change pace, weave density and view, scrub through time, and swap in five other planetary pairs, each with its ratio and loop count worked out from the same twelve numbers. A short two-column essay insists, calmly, that it is all only division. VISUAL TECHNIQUES - Canvas line accumulation at very low alpha with per-line jitter of weight and opacity, so dense regions darken like cross-hatching; a second canvas layer for the red re-drawing - Inline SVG instruments over the canvas: degree ring with 360 generated ticks, orbit circles ticked by stroke-dasharray, engraved Sun, compass rose, planets, live chord, scrub hairline - SVG textPath labels curved along the orbits, with paper-coloured halos so they stay legible over the weave - feTurbulence paper grain and foxing, feDisplacementMap wobble on engraved linework for ink irregularity - CSS laid-paper chain lines, inset-shadow plate-mark emboss, flickering candle vignette - Star border from an SVG pattern of six-armed asterisks with drawn corner stars - Engraved title typography in Baskerville-family system serifs with old-style numerals, small caps, drop cap and justified narrow columns - SVG swash flourishes drawn in by stroke-dashoffset; spring-eased marks, knob and thumbnail motion - Procedurally built year ruler (alternating scale bar, ticks, numerals) rebuilt for each pair and width - Continued-fraction computation of the nearest simple period ratio, loop count and closure error for each pair - Thumbnails rendered by the same drawing routine as the main plate, in whichever view is active INTERACTION MODEL The drawing begins on load. "Stay the pen" pauses and resumes (Space also works); "Begin anew" restarts. The engraved knob is dragged, scrolled, or turned with arrow keys through seven paces, from ten years per second down to true real time. The Weave slider sets the interval between lines from 1 to 20 days and the figure is re-ruled at once. Three radio buttons switch between Lines (the chords), Path (the other planet's path seen from a fixed Earth, with the Sun circling and retrograde loops) and Midpoints (the locus of chord midpoints); the thumbnails follow the chosen view. Moving the pointer, or dragging a finger sideways, across the plate temporarily shows the figure and planets at the date under the pointer, with a hairline dropping to the ruler and a readout such as "Year 3, day 112 · Venus 47° ahead"; leaving the plate returns to the live drawing. Dragging the red index on the ruler, or focusing it and using arrow, Page, Home and End keys, sets the date permanently. Choosing a small plate swaps that pair into the main plate, resets the weave and pace to suit its cycle, and rewrites the key, ratio, ruler and caption. After completion and a few idle seconds the following cycle is drawn over in red. With reduced motion the completed figure is shown at once, without entrance animation, flicker or red re-drawing, and all controls and the scrubber remain available.