Gallery

Generated works

The most recent works saved in Studio.

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Catalogue

All sketches (44)

Every video starts from one of these mathematical systems, drawn in real time in the browser.

Curves

Hypocycloids — Curves traced by a point on a small circle rolling inside a larger one. The r/R ratio decides whether you get deltoids, astroids, or spirographs.

Hypocycloids

Curves traced by a point on a small circle rolling inside a larger one. The r/R ratio decides whether you get deltoids, astroids, or spirographs.

Epicycloids — A circle rolls along the outside of another: the tracked point draws cardioids, nephroids and other elegant curves found in optics and mechanics.

Epicycloids

A circle rolls along the outside of another: the tracked point draws cardioids, nephroids and other elegant curves found in optics and mechanics.

Lissajous — Two perpendicular oscillations combined. The frequency ratio and phase determine shapes from simple ellipses to intricate woven knots.

Lissajous

Two perpendicular oscillations combined. The frequency ratio and phase determine shapes from simple ellipses to intricate woven knots.

Rose curves — Polar curves of the form r = cos(kθ): symmetric petals whose count depends on the parity of k. Mathematics draws exact flowers.

Rose curves

Polar curves of the form r = cos(kθ): symmetric petals whose count depends on the parity of k. Mathematics draws exact flowers.

Maurer Rose — A polar rose sampled at regular intervals, with points joined by straight lines. Hidden moirés and symmetries emerge from the numbers.

Maurer Rose

A polar rose sampled at regular intervals, with points joined by straight lines. Hidden moirés and symmetries emerge from the numbers.

Butterfly — Fay's transcendental curve, expressed in polar coordinates with exponentials and sines. A mathematical butterfly from a single equation.

Butterfly

Fay's transcendental curve, expressed in polar coordinates with exponentials and sines. A mathematical butterfly from a single equation.

Spirals — Archimedean, logarithmic, Fermat, Cornu: each spiral has its own radial growth law, from the seashell to the clothoid transition curve.

Spirals

Archimedean, logarithmic, Fermat, Cornu: each spiral has its own radial growth law, from the seashell to the clothoid transition curve.

Phyllotaxis — Sunflower seeds placed at the golden angle (137.5°) with radius √n. The same algorithm nature uses to pack seeds optimally.

Phyllotaxis

Sunflower seeds placed at the golden angle (137.5°) with radius √n. The same algorithm nature uses to pack seeds optimally.

Superformula — The Gielis superformula (2003): a single polar equation that, by varying four parameters, generates starfish, diatoms, flowers and shells. Its continuous metamorphosis shows how many living forms share the same mathematics.

Superformula

The Gielis superformula (2003): a single polar equation that, by varying four parameters, generates starfish, diatoms, flowers and shells. Its continuous metamorphosis shows how many living forms share the same mathematics.

Fractals & Chaos

Harmonograph — Damped pendulums oscillating against each other: evolving Lissajous figures that slowly fade as friction takes over.

Harmonograph

Damped pendulums oscillating against each other: evolving Lissajous figures that slowly fade as friction takes over.

Attractors — Strange attractors: chaotic trajectories that never repeat, yet stay confined to fractal structures: order within disorder.

Attractors

Strange attractors: chaotic trajectories that never repeat, yet stay confined to fractal structures: order within disorder.

Double Pendulum — The hallmark of chaos theory: two rods joined by a pivot. Tiny differences in starting conditions produce wildly divergent paths.

Double Pendulum

The hallmark of chaos theory: two rods joined by a pivot. Tiny differences in starting conditions produce wildly divergent paths.

Lorenz — The Lorenz attractor, the butterfly of chaos theory: nearly identical trajectories tear apart within seconds, yet stay trapped on the same two wings. Deterministic, never repeating.

Lorenz

The Lorenz attractor, the butterfly of chaos theory: nearly identical trajectories tear apart within seconds, yet stay trapped on the same two wings. Deterministic, never repeating.

Julia Set — A morphing Julia set: the parameter c travels a closed orbit in the complex plane while z → z² + c folds and unfolds infinite filigree, looping seamlessly.

Julia Set

A morphing Julia set: the parameter c travels a closed orbit in the complex plane while z → z² + c folds and unfolds infinite filigree, looping seamlessly.

L-Systems — Recursive fractals generated by Lindenmayer systems: simple rules produce trees, snowflakes and space-filling Hilbert curves.

L-Systems

Recursive fractals generated by Lindenmayer systems: simple rules produce trees, snowflakes and space-filling Hilbert curves.

Reaction-Diffusion — Gray-Scott reaction-diffusion: two chemical species U and V that interact to grow spots, mazes, coral and waves, the Turing patterns of 1952.

Reaction-Diffusion

Gray-Scott reaction-diffusion: two chemical species U and V that interact to grow spots, mazes, coral and waves, the Turing patterns of 1952.

Three-Body — The three-body problem: three masses in mutual gravitational free-fall, from the perfect Chenciner-Montgomery figure-eight to Burrau's chaos. No closed formula solves it: only numerical integration reveals its choreographies.

Three-Body

The three-body problem: three masses in mutual gravitational free-fall, from the perfect Chenciner-Montgomery figure-eight to Burrau's chaos. No closed formula solves it: only numerical integration reveals its choreographies.

Sandpile — The abelian sandpile of Bak, Tang and Wiesenfeld: grains dropped one by one onto a grid; any cell reaching 4 topples onto its neighbours, unleashing avalanches at every scale. Out of the chaos grows a perfectly deterministic fractal mandala (1987).

Sandpile

The abelian sandpile of Bak, Tang and Wiesenfeld: grains dropped one by one onto a grid; any cell reaching 4 topples onto its neighbours, unleashing avalanches at every scale. Out of the chaos grows a perfectly deterministic fractal mandala (1987).

Collatz Coral — Thousands of Collatz (3n+1) sequences retraced backwards from 1: even turns clockwise, odd counter-clockwise, and shared prefixes redraw the same trunk until a glowing coral emerges. A conjecture open since 1937.

Collatz Coral

Thousands of Collatz (3n+1) sequences retraced backwards from 1: even turns clockwise, odd counter-clockwise, and shared prefixes redraw the same trunk until a glowing coral emerges. A conjecture open since 1937.

Buddhabrot — The Buddhabrot: every orbit escaping z² + c deposits its whole path into a density map. Millions of orbits later, a seated luminous figure emerges from the noise. A live Monte Carlo render (Melinda Green, 1993).

Buddhabrot

The Buddhabrot: every orbit escaping z² + c deposits its whole path into a density map. Millions of orbits later, a seated luminous figure emerges from the noise. A live Monte Carlo render (Melinda Green, 1993).

Magnetic Pendulum — A pendulum over three magnets: which one will capture it? Every pixel is a starting point, coloured by the answer. A fractal map emerges with endlessly interleaved boundaries: Newtonian physics, unpredictable outcome.

Magnetic Pendulum

A pendulum over three magnets: which one will capture it? Every pixel is a starting point, coloured by the answer. A fractal map emerges with endlessly interleaved boundaries: Newtonian physics, unpredictable outcome.

DLA Crystal — Diffusion-limited aggregation: Brownian particles freeze at first contact with the growing cluster. Three lines of rules and a fractal snowflake is born (Witten and Sander, 1981).

DLA Crystal

Diffusion-limited aggregation: Brownian particles freeze at first contact with the growing cluster. Three lines of rules and a fractal snowflake is born (Witten and Sander, 1981).

Optical Illusions

Moving Illusions — Rotating snakes, lilac chaser, café wall: static patterns the brain interprets as motion or distortion.

Moving Illusions

Rotating snakes, lilac chaser, café wall: static patterns the brain interprets as motion or distortion.

Bistable Motion — A cylinder of dots rotating with no depth cues: half of all viewers see it spin clockwise, the other half counter-clockwise — and both are right. Bistable perception: when the data underdetermines, the brain decides.

Bistable Motion

A cylinder of dots rotating with no depth cues: half of all viewers see it spin clockwise, the other half counter-clockwise — and both are right. Bistable perception: when the data underdetermines, the brain decides.

Color Illusions — Two areas with the exact same RGB that look like different colours: Adelson's checker-shadow, simultaneous contrast, Munker-White spheres. When the animated proof connects them, the brain refuses to believe it: we don't see light, we see an interpretation.

Color Illusions

Two areas with the exact same RGB that look like different colours: Adelson's checker-shadow, simultaneous contrast, Munker-White spheres. When the animated proof connects them, the brain refuses to believe it: we don't see light, we see an interpretation.

Pinna Rotation — The Pinna-Brelstaff illusion: rings of tilted elements that seem to counter-rotate as the pattern zooms in and out. Yet physical rotation is exactly zero: only the scale changes, the rotation happens in your motion detectors (2000).

Pinna Rotation

The Pinna-Brelstaff illusion: rings of tilted elements that seem to counter-rotate as the pattern zooms in and out. Yet physical rotation is exactly zero: only the scale changes, the rotation happens in your motion detectors (2000).

Ebbinghaus — The dynamic Ebbinghaus illusion: the central circle never changes size, but as the surrounding circles swell and shrink it visibly seems to breathe. Mid clip a dashed reference ring proves it: context decides perceived size (1898).

Ebbinghaus

The dynamic Ebbinghaus illusion: the central circle never changes size, but as the surrounding circles swell and shrink it visibly seems to breathe. Mid clip a dashed reference ring proves it: context decides perceived size (1898).

Patterns

String Art — Points around a circle connected via modular times tables. From simple multiplication mod n, cardioids, nephroids and mandalas emerge.

String Art

Points around a circle connected via modular times tables. From simple multiplication mod n, cardioids, nephroids and mandalas emerge.

Line Dance — Two hundred parametric lines chasing each other as k morphs: from a singular point emerge triskelia, mandalas and multi-fold fans.

Line Dance

Two hundred parametric lines chasing each other as k morphs: from a singular point emerge triskelia, mandalas and multi-fold fans.

Interferenza — Circular waves adding and cancelling. Where crests meet, bright fringes; where they oppose, silent nodes.

Interferenza

Circular waves adding and cancelling. Where crests meet, bright fringes; where they oppose, silent nodes.

Fourier — Any periodic motion is a sum of rotating circles. Fourier's theorem made visible, in real time.

Fourier

Any periodic motion is a sum of rotating circles. Fourier's theorem made visible, in real time.

Fourier Drawing — Drawing any icon by composing dozens of rotating epicycles. Fourier's theorem reconstructs the signal point by point.

Fourier Drawing

Drawing any icon by composing dozens of rotating epicycles. Fourier's theorem reconstructs the signal point by point.

Flow Field — Particles carried by a Perlin-noise field. Chaos becomes flow, flow becomes brushstroke.

Flow Field

Particles carried by a Perlin-noise field. Chaos becomes flow, flow becomes brushstroke.

ASCII Walker — A walking human figure made of letters and digits, animated frame by frame. Typography in motion.

ASCII Walker

A walking human figure made of letters and digits, animated frame by frame. Typography in motion.

Particle Walker — A walk composed entirely of particles: the silhouette appears only where orbits cross.

Particle Walker

A walk composed entirely of particles: the silhouette appears only where orbits cross.

ASCII Art — An image converted to typographic characters: pixel luminance maps to glyph density.

ASCII Art

An image converted to typographic characters: pixel luminance maps to glyph density.

ASCII Frog — An ASCII frog catches flies with its tongue. Minimal animation inspired by the typographic culture of the web.

ASCII Frog

An ASCII frog catches flies with its tongue. Minimal animation inspired by the typographic culture of the web.

Night Garden — A procedural garden blooming in the night: stars, stems, leaves, petals and grass emerge in sequence while fireflies dance over the finished scene.

Night Garden

A procedural garden blooming in the night: stars, stems, leaves, petals and grass emerge in sequence while fireflies dance over the finished scene.

Mandala — Mandala with n-fold radial symmetry: each ring picks a motif (spoke, arc, petal, diamond) and the figure replicates around the centre, with optional mirroring for full dihedral symmetry.

Mandala

Mandala with n-fold radial symmetry: each ring picks a motif (spoke, arc, petal, diamond) and the figure replicates around the centre, with optional mirroring for full dihedral symmetry.

Kaleidoscope — A kaleidoscope: three angled mirrors multiply a handful of colourful shapes into endless patterns. Projective geometry turned into play.

Kaleidoscope

A kaleidoscope: three angled mirrors multiply a handful of colourful shapes into endless patterns. Projective geometry turned into play.

Chladni — Chladni figures: thousands of grains on a vibrating plate flee the moving regions and settle along the silent nodal lines. At every mode change the sand snaps into a new symmetric figure (1787).

Chladni

Chladni figures: thousands of grains on a vibrating plate flee the moving regions and settle along the silent nodal lines. At every mode change the sand snaps into a new symmetric figure (1787).

Physarum — Physarum polycephalum: thousands of chemotactic agents deposit and follow a trail that diffuses and evaporates. From purely local feedback — sense, turn, deposit — a living filament network self-organises, the same web the slime mould uses to solve mazes.

Physarum

Physarum polycephalum: thousands of chemotactic agents deposit and follow a trail that diffuses and evaporates. From purely local feedback — sense, turn, deposit — a living filament network self-organises, the same web the slime mould uses to solve mazes.

Differential Growth — Differential growth: a closed curve feeds, stretches and folds onto itself under cohesion and repulsion forces. Node after node, coral-like lace emerges — the same morphogenesis that shapes living tissue.

Differential Growth

Differential growth: a closed curve feeds, stretches and folds onto itself under cohesion and repulsion forces. Node after node, coral-like lace emerges — the same morphogenesis that shapes living tissue.

Murmuration — A leaderless starling flock: each bird follows just three local rules — separate, align, cohere with its neighbours — and out of nothing emerge the collective sky-dances of dusk. Reynolds' boids model (1987).

Murmuration

A leaderless starling flock: each bird follows just three local rules — separate, align, cohere with its neighbours — and out of nothing emerge the collective sky-dances of dusk. Reynolds' boids model (1987).