About SacredForm

1 · Nearly a hundred figures in 2D, 3D and 4D

Explore

Every figure is stored as points in four dimensions, so one Dimension dial moves between them. A flat figure tilts off the page and grows into its solid: the Flower of Life into the densest packing of spheres, the hexagram into the star tetrahedron. A solid lifts into four dimensions, or flattens into its exact shadow.

Figures draw themselves with compass-style construction, and each one rings at the frequencies of its own edges, so you can hear the chord of a shape. Cut any solid with a plane, or any 4D polytope with a hyperplane, and watch the cross-section sweep through. Export line art as SVG for pen plotters and laser cutters, a 3D-printable STL or OBJ, or a poster.

Open Explore Read about every figure

2 · Ten narrated passages through the ideas

Journeys

Genesis, The Golden Thread, Into the Fourth Dimension, The Plane Rises, Flatland, The Breathing Solid, Sound Made Visible, The Archimedean Family, Kepler’s Stars and The Builders’ Measures. Each step moves: figures draw themselves, rise from the page, turn and slice, and the narration can be read aloud.

You can also make your own: string figures together with captions, lifts and slices, and share the whole journey as a link.

Open Journeys Read the journeys

3 · Compass and straightedge, the way Euclid did it

Construct

Twenty lessons, from the vesica piscis and Euclid’s first proposition to the golden cut, Ptolemy’s pentagon and Metatron’s Cube. Intersections are exact, every crossing snaps, and hints come one move at a time. Then come twenty-two challenges with a par and no teaching, from dropping a perpendicular to doubling the square as in Plato’s Meno.

Replay redraws a solved construction stroke by stroke with compass, ruler and pencil, and Blueprint saves it as a drafting sheet. In the sandbox, measuring two lengths lights up the ratios they make: φ, √2, √3.

Open Construct Follow the constructions step by step

4 · Sound made visible

Cymatics

A Chladni plate with some forty thousand grains of sand, square, round or triangular, driven by a tone, by your voice through the microphone, or by the chord of a figure from Explore. Find the figures sweeps the pitch and stops on each resonance, naming its mode.

Beside the plate are water ripples, spherical harmonics, a monochord, a harmonograph with two-pendulum, rotary and three-pendulum machines, and the Lambdoma, the Pythagorean table of ratios, to play and build chords on.

Open Cymatics

5 · The music of the spheres

Spheres

Dance draws a line between two planets on their real orbits every few days: Earth and Venus trace a five-petalled rose over eight years, and Jupiter and Saturn the triangle of the Great Conjunctions. Harmony plays Kepler’s planetary songs from their real speeds and checks his third law as they move. Rhythm turns polygons, star polygons and Euclidean rhythms into rings of polyrhythm.

Open Spheres

6 · Draw with symmetry

Studio

A mandala studio with 1 to 32-fold symmetry and mirrors, brush, line, compass and petal tools, stained-glass fills and sacred guides to snap to. Pattern mode repeats your drawing across the whole plane by any of the seventeen wallpaper groups, and saves a seamless tile.

Every stroke sings as you draw it, a music-box arm plays the finished mandala, and Lift into 3D turns it into a dome, a vessel or a crystal. Save it as PNG, SVG or video, or share it as a link that carries the whole drawing.

Open Studio

7 · A timed sitting

Contemplate

From one minute to an hour. A singing bowl opens the sitting, then figures rise slowly one into the next over a drone that glides through each one’s chord, while a ring paces your breath: coherent, 4-7-8, box breathing, cyclic sighing or no guide at all. Optional bells mark the minutes, and a quiet record of your sittings stays on your device.

Open Contemplate