Pearl Lace
Circles reflected through circles become intricate necklaces. Quiet openings hold the composition while tiny pearls collect around their edges.
All pattern generators
Explore the mathematics, choose a starting composition, then make it your own. Each instrument offers editable controls and SVG or PNG export.
Browse the visual gallery →Orbital Packing
A few generous circles give way to constellations of smaller ones. Tangency creates a continuous rhythm, with soft neutral discs adding weight and depth.
Julia Filigree
Twin curls, branching islands and finely engraved edges emerge from a single complex number. Nested contours trace their changing silhouette.
Recursive Coral
A sculptural fan grows from a single stem. Tapered branches overlap like layers of cut paper, opening into a delicate crown.
Triangular Weave
One continuous path folds into a triangular labyrinth. Soft corners and a tonal underlay give the recursive weave a tactile, carved quality.
Heart Echoes
A heart opens into a delicate tunnel of nested contours. Twisting layers and a travelling pulse turn a familiar symbol into a sculptural line study.
Möbius Ribbons
Parallel strands trace a band with a half twist. One continuous surface turns inside out as you orbit its woven form.
Catenoid
A quiet hourglass built from circular contours. Its waist opens into the minimal surface formed by a suspended soap film.
Superellipsoid
A rounded cube softens into a sphere and pinches into a faceted jewel. Continuous contours expose the changing silhouette.
Lissajous Weave
Interlocking harmonic traces form a floating woven knot. Small phase offsets create depth and ribbons of negative space.
Logarithmic Shell
Fine ribs follow an expanding spiral tube. Exponential growth draws a sculptural shell from a compact mathematical rule.
Guilloché
Nested rosettes interfere in an intricate engraved medallion. Phase-shifted radial waves create delicate security-print linework.
Block Relief
A landscape built from isometric blocks. Stepped hills, hollow craters and travelling waves turn a square lattice into sculptural linework.
Azulejo Rosettes
Scalloped flowers and curved diamonds grow from a repeating ornamental field. Nested ink lines give each tile a delicately engraved rhythm.
Woven Stars
Interlaced square ribbons form eight-pointed stars. Fine parallel strands carry a quiet pulse through alternating over-and-under crossings.
Diamond Relief
Fine ruled facets turn a tiled surface into a field of raised diamonds. Peaks rise, flatten and invert in a slow travelling wave.
Tile Drift
A field of ornamental tiles gathers into a fluid swirl, then settles back into symmetry. Move its centre to pull the geometry across the page.
Lava Folds
Ropes of cooling lava buckle into overlapping folds. A travelling compression wave moves through a broad tongue, a narrow stream or a branching fan.
Vortex Wake
A current flows past a cylinder and sheds a Kármán vortex street, simulated with vortex particles. Dye rolls up into the spirals of a smoke tunnel; drag the cylinder to move the wake.
Contour Type
Letters become a landscape of nested contours. Neighbouring outlines meet, merge and breathe as a slow wave passes through the word.
Liquid Type
A word drawn in fine ribbons softens into a flowing sheet. Letters shear, ripple and pull apart, hovering between readable type and abstract linework.
Reaction Fields
Two reacting, diffusing chemicals grow into islands and labyrinths. Watch cells spread, divide and meet, then scrub back to a composition worth keeping.
Topography
Equal-height lines trace an imagined landscape. A mountain, a crater or a long ridge is folded by smooth noise into islands of nested contours.
Harmonic Shells
A spherical harmonic pushes a sphere into lobes. Latitude contours describe its surface like topographic lines wrapped around a sculpture.
Hopf Fibres
Circles from a four-dimensional sphere project into a linked bundle. Every pair is linked once; a chosen band of fibres becomes a flowing, hollow sculpture.
Harmonograph
Two damped oscillations draw a slowly closing weave. A second, slightly detuned pair opens the threads into folds, a mathematical version of a pendulum drawing machine.
Moiré
Two regular drawings overlap. Their slight mismatch creates broad bands that belong to neither layer. Drag the second layer, or turn it a fraction, and the apparent pattern changes.
Torus Knots
A closed curve winds around a torus in two directions. Parallel strands make a sculptural ribbon; small breaks at crossings reveal which strands pass in front.
Spirograph
A point rides a circle rolling around another circle. Nearby pen positions build a family of fine traces, turning the familiar rosette into an engraving.
Chladni Figures
Sand on a vibrating plate gathers along its still lines. Here an idealised standing-wave field reveals those lines directly, with nearby contours forming a delicate echo.
Lorenz Attractor
The butterfly of chaos: one trajectory turns between two lobes without repeating. A selected stretch of its path and a little depth fading reveal an airy, folded structure.
Interference
Two radial waves meet. Their amplitudes add; lines trace equal values of the combined field. Move either source to reshape the drawing.
Flow Field
Long, evenly seeded currents gather into folds of silk. A smooth noise displacement bends each strand while leaving room for the drawing to breathe.
Sine Waves
Layered harmonics form a rippling sheet. Phase offsets pull parallel strands into luminous folds and open pockets of negative space.
Voronoi Flow
A cellular engraving: continuous currents pass through irregular Voronoi islands, separated by fine channels of open space.
Quadtree Flow
Nested rooms hold quarter-circle currents. Changing scales and orientations turn a recursive grid into a rhythmic architectural engraving.
Geodesic Polyhedron
A Platonic solid, geodesically subdivided, drawn as 2D line art. Detail is subdivision; turn and tilt choose the view. Far side fades the hidden hemisphere so the solid reads in depth.
Streamlines
A seed is followed through the field until it leaves the sheet or nears an existing line. Finished lines propose new seeds at a fixed offset: even spacing, not clumps.
Truchet Tiles
A square grid of quarter-circle pairs. Each tile flips by seed, so the sheet reads as one continuous maze of arcs.
Iso Cubes
An isometric cube lattice. Height is rolled per cell from the seed, so the grid reads as a scattered city of boxes.
Terrell Cubes
Cubes photographed as they rush past at near light speed. They are shorter in motion, yet the camera shows them turned, not squashed: the Terrell–Penrose effect, computed exactly.
Tumbling Blocks
A rhombille tiling: each hexagon is three rhombi, and the sheet reads as a stack of cubes.
Penrose Tiles
Kites and darts that cover the plane without ever repeating. Five-fold symmetry, golden-ratio edges, and no translational grid.
Hat Tile
A 13-sided polykite, the hat, that tiles the plane but never periodically. The first aperiodic monotile; Spectre later dropped the reflections.
Nested Polygons
Concentric n-gons, each rotated a little further than the last. Sides, layers, and twist are the whole drawing.
Triangular Mosaic
A tessellation of equilateral triangles. Fill is the chance a face is inked rather than outlined.
Noise Field
Horizontal hatches displaced by simplex noise. The drawing is the noise itself, with no particles, no field walking.
Warped Grid
A regular lattice, each vertex shoved by simplex noise. The drawing is the grid’s own edges after the shove: a cloth, not a triangulation of random sites.
Circle Packing
Greedy packing: drop a circle, keep it if it fits. Radius range and gap set how tight the colony gets.
Voronoi Cells
Sites from the seed, cells from the nearest-site rule. Some cells fill with copies of themselves, each ring an even step inside the last, like the rings of a contour map.
Hex Mosaic
A pointy-top hex grid. Fill is the chance a cell is inked rather than outlined.
Phyllotaxis
Vogel’s sunflower: each seed sits on a golden-angle spiral. Count fills the disc; spread is how far the pack reaches.
Spiral
Archimedean arms: radius grows linearly with angle. Turns wind the coil; arms is how many start equally around the origin.
Fibonacci Spiral
Squares whose sides are the Fibonacci sequence. A quarter-circle in each chamber is the golden spiral; an inset at 1/φ is the septum.
Delaunay Mesh
The dual of Voronoi: every site joins its neighbours into triangles. Same seed and site count as Voronoi Cells gives the matching mesh.
Hex Truchet
Each hex picks one of two arc orientations. Adjacent edge midpoints join with 120° arcs so paths continue across the honeycomb.
Ripples
Concentric rings from one or more sources. Wavelength is the gap between crests; sources scatter from the seed.
Hilbert Curve
A space-filling curve of the given order. Rotation turns the square; the path always visits every cell once.
Koch Snowflake
Each side of an equilateral triangle is replaced by a four-segment bump. Iterate and the perimeter grows without bound inside a finite area.
Mandelbrot Set
Iterate z → z² + c in the complex plane. The boundary is infinitely crumpled; zoom is a window onto that edge, drawn as contour lines.
Barnsley Fern
Four affine maps, chosen at random, iterate a point. The attractor is a fern: self-similar fronds from a handful of matrices.
Self-Truncate
A Platonic seed, truncated toward rectification, then truncated again. Amount is how far each cut goes; rounds is how many times the solid eats itself.
Irregular Deltahedra
A convex hull of seeded points on a sphere. Every face is a triangle, none of them regular. Count is how many vertices; jitter breaks the even packing.
Column Capital
A circular shaft has to meet a square bay. Nested superellipses are the in-between family: p = 2 is the column, large p is the abacus.
Universal Joint
A dovetail revolved around its axis becomes a concave disk. Columns can then meet at irregular angles: a 3D joint from a 2D fastener.
Dovetail Course
Pins and tails along a seam: the planar ancestor of the universal joint. Flare is how hard the lock bites; columns is how many keys fit the run.
Superellipse
One exponent carries a shape from diamond through circle to near-square. Sweep it across a grid, or nest the whole range inside a single frame.
Gosper Curve
A single line that fills a hexagon and never crosses itself. Far away it is a texture; up close it is one continuous path you can follow end to end.
Differential Growth
A closed loop that gains length faster than its enclosure allows, so it has to fold. The same rule shapes lettuce edges, coral rims and the cortex.
Halftone Field
A regular screen of dots where only the size carries the picture. Turn the screen off-axis, change the field beneath it, and tone becomes texture.
Star Rosettes
Islamic star patterns drawn the way the craftsmen did: lines leave the midpoint of every tile edge at one fixed angle and run until they meet. One slider changes the order of every star at once.
Magic Angle
Two identical honeycomb sheets, one turned by a degree or so. Their mismatch builds a second lattice hundreds of times larger than either, and near 1.1° that superlattice is where the physics happens.
Decagonal Strapwork
Ten-fold star patterns on a tiling that never repeats. Two rhombus shapes carry the same strapwork rule as the periodic panels, but nothing about the arrangement comes back around.
Poincaré Disk
Every tile here is the same size. The whole infinite hyperbolic plane is drawn inside one circle, and the rim is infinitely far away, so the tiles appear to shrink as they approach it.
Cellular Automata
One row of cells, one rule, and the row below follows from the three cells above it. Eight bits of instruction are enough to produce order, chaos or something that does both at once.
Multi-scale Truchet
Truchet's tiles, but each square may break into four smaller ones before it decides which way to turn. Arcs still meet at every edge midpoint, so coarse and fine areas join without a break.
Conformal Spiral
A square grid pushed through the exponential map. Angles survive the journey intact, so every crossing stays square while the whole sheet winds into a spiral that never quite arrives.
Kolam
A line that threads a field of dots, never crossing a dot and never leaving a loose end. Drawn at dawn on doorsteps across South India, and closed by arithmetic rather than by eye.
Café Wall
Offset rows of blocks divided by thin mortar. Every row is exactly horizontal, and almost nobody sees them that way.
Zöllner Lines
Long parallels crossed by short strokes that lean one way, then the other. The parallels lean with them.
Scintillating Grid
Pale bars with a disc at every crossing. Dark spots appear in the discs you are not looking at, and never in the one you are.
Peripheral Drift
Nothing here moves. Each band runs dark to light the same way round, and the field creeps sideways whenever you look past it.
Necker Lattice
A field of wireframe cubes with nothing to say which face is nearer. Stare, and the whole field turns inside out at once.
Fraser Spiral
Concentric circles built from leaning cords. Trace one with a finger and it closes; let go and it winds inward again.
Op Bulge
A flat grid, pushed outward from the middle. The page stays flat and a sphere sits on it anyway.
Kanizsa Contours
Discs with a bite taken out of each. The shape between them has edges, a surface and a brightness, and none of it is drawn.
Penrose Tribar
Three arms of cubes, each turning a square corner on the last, arriving back where they began. Follow any arm and it is ordinary.
Vanishing Corridor
Frames receding to a single point, each one the same size as the last and none of them the same on the page.
Coffered Vault
A ceiling of sunk panels. Every recess is cut the same way, and the four sides of each take their own tone.
Tiled Floor
A chequered pavement running to the horizon. Every tile is square and no two are drawn the same shape.
Corrugation
Ruled lines that crowd where the sheet turns away and open where it faces you. Nothing is shaded; the spacing does all of it.
Cube of Cubes
A cube of small cubes with a pile taken out of its corner, lit by a low sun. Every pile that fits is a plane partition, and seen from the corner each one tiles a hexagon with rhombi.
Hitomezashi
Running stitches along every row and column, each starting a half step in or not. The boxes and crosses that appear were never stitched.
Quasicrystal
Five or seven flat waves laid over one another at equal angles. Order everywhere, and the same patch never twice.
Dot Relief
One dot per cell, sized by a surface nobody drew. The grid is dead flat and the sheet rolls like beaten metal.
Basket Weave
Pairs of planks laid at right angles, turn and turn about. Flat on the page, and it will not stop going over and under.
Flower of Life
Circles of one size, each through the centres of its neighbours. Every petal, lens and six-pointed star in it is an accident of the overlap.
Celtic Plait
Two families of bands crossing on the diagonal, each one over, then under, without exception. No band ever ends.
Chevron Field
Bands of zigzag, every one the same and every other one a shade apart. The eye reads the pairs as ridges and folds the sheet.
Albers Squares
Squares inside squares, sitting low in the frame. Each step of tone is equal, and none of them look it.
Dragon Curve
One strip of paper folded in half the same way over and over, then opened out to right angles. It never crosses itself.
Menger Face
A cube whose three visible faces have had their middles removed, and the middles of what is left, and so on.
Sunburst
Wedges from a point, every other one inked. Straight edges throughout, and the field will not stay flat.
Steiner Chain
A ring of circles, each touching its neighbours and both of the circles it lies between. Either it closes exactly or it never does.
Rose Window
Mullions out to the rim, and at every ring a course of foils sized to close the gap exactly.
Apollonian Gasket
Three circles that touch, and the one circle that fits between them, and then the three new gaps, without end.
Moiré Circles
Two sets of rings, drawn a little apart. Where they disagree, a second family of curves appears that neither one contains.
Lissajous Grid
A plate of figures, one for every pair of whole-number frequencies. The ratio is legible from the shape alone.
Truchet Triangles
The original Truchet tile: a square cut on its diagonal, one half dark. Four turns of it, arranged by rule, give diamonds, chevrons and pinwheels.
Turing Pattern
Two chemicals, one spreading faster than the other, settle into spots, mazes or coral from an almost uniform start. No edge anywhere, so it repeats forever.
Parallel Curves
A bundle of strands that runs straight, turns a tight corner, and runs on, every strand the same distance from its neighbours the whole way round.
Seigaiha
Fans of concentric arcs in overlapping rows, each row laid over the last. Only the top of every fan survives, and the field turns into swell.
Helicoid
A spiral staircase of straight lines, the shape a soap film takes on a twisted wire. Bend it and it rolls up into a catenoid without stretching a single line.
Helix Lantern
A sphere sliced into floating rings, each strung with circles that crowd to one side. The crowded edges climb the globe as a glowing spiral.
Bauhaus Blocks
Squares that round off some corners and keep others. Drops, leaves, arches and circles fall out of one choice per corner, set in a strict grid.
Jessen's Icosahedron
Twenty triangles whose every pair of neighbours meets at a right angle. Six pairs fold into deep notches, so a regular icosahedron turns star-like.
Pythagoras
A right triangle with a square on each side. Count the cells: the two smaller squares together hold exactly as many as the largest.
Lattice Knots
Closed loops of square bar that only ever run along the edges of a cube grid. Three tones are all it takes to read them as solid.
Heesch Numbers
A shape that cannot tile the plane, surrounded by rings of its own copies until no further ring will close. The count of rings is its Heesch number.
Flipdot
A board of flip discs turned over by a fluid field moving beneath it. Fast edges leave discs caught mid-flip, squashed to slivers.
Talbot Carpet
Light passing through a row of slits rebuilds the row further on, and in between splits into finer and finer copies of it. Followed downstream, the field weaves a fractal lace.
Spectre
A single tile that covers the plane without ever repeating, using copies that are only turned, never flipped. Bend its edges and it cannot be flipped at all.
Euler Spiral
A curve that bends a little more with every step, winding from a straight middle into two tightening eyes. The same curve eases trains and roads into their bends.
Coxeter Frieze
Rows of whole numbers held between two rows of 1s, every diamond of four obeying one rule. Each such frieze comes from a polygon cut into triangles, drawn above it.
Stomachion
Archimedes' square of fourteen pieces, every corner on a 12 × 12 grid. In motion it comes apart, turns, and closes up again.
Game of Life
A grid of cells living and dying by three rules. Fading trails show where things were going: gliders streaming from Gosper's gun, or five cells that churn for a thousand turns.
Pinwheel
One right triangle, legs one and two, cut again and again into five smaller copies of itself. Its tiles end up pointing in infinitely many directions.
Interlock
A plain grid of squares whose shared edges bend across the sheet until the tiles lock together like creatures. However far they bend, every tile still fits its neighbours exactly.
Times Table
Points round a circle, each joined to the point its number is multiplied to. The straight chords bend into a cardioid at times two, a nephroid at times three, and ever stranger curves between.
Folded Paper
A crumpled sheet drawn only in parallel lines. Each facet is hatched as a fan from its peak, the lines packed tighter the further it turns from the light, so the folds appear with no shading at all.
Maze Quarters
A sheet split into quarters, each on its own grid at its own angle and filled with one maze. Drawn as its paths, every maze branches like the streets of an old town.
Packed Cubes
A hexagonal field of cubes, each cut again and again into boxes along its own small grid. Thin gaps between the boxes show the pieces packed inside.
Unsettled
A grid of squares in perfect order at one end, each square turned and shifted a little more along the sheet, until the far rows lie scattered.
Iso City
A city in isometric view: blocks cut into lots, towers rising towards downtown, a river under its bridges, and one sun casting every shadow.
Bloom
A polygon ringed with Yoshimura creases that folds from a flat sheet through a bowl to a flat stack the size of its centre, like a flower closing.
Routes
Graph theory on a road network: Dijkstra's shortest path from A to B with real alternatives, a minimum spanning tree, or Euler's one round of every road.
Sandpile
Grains poured on one square of a grid, where any square holding four topples and gives one to each neighbour. They settle into a fractal mandala, the same whatever order the squares topple in.
Recamán Arcs
Steps of one, two, three and on along the number line, each back towards zero if it lands somewhere new and forwards if not, every step a half circle. The arcs nest into shells that never quite settle.
Aztec Diamond
A diamond of squares covered by dominoes, chosen fairly from every way to do it, drawn as the paths hidden in it. Outside a circle everything freezes into straight lines; inside it the paths wander like ridges.
Moser Spindle
Seven points and eleven edges, every edge one unit long, that three colours cannot colour. So a plane coloured to keep points one apart different needs four colours at least; seven are enough.
Knight's Tour
A chess knight visits every square of the board exactly once, and its path of short, crooked jumps becomes a dense star of lines.
Ford Circles
Above every fraction sits a circle, the smaller the bigger its denominator. Neighbouring fractions' circles touch, and no two ever overlap, so the rationals become a lace that never ends.
Kepler's Cosmos
The five Platonic solids nested one inside another, with a sphere between each pair: Kepler's 1596 model of why there were six planets, and why they sat where they did.
Pulsar Plot
Eighty radio pulses from a spinning star, stacked one above the next, each hiding the ones behind it. A chart from a 1970 thesis that became a landscape.
Tesseract
A four-dimensional cube turning through a direction we cannot point to. Its far cube swells, passes through the near one and turns inside out, edges never bending.
Superformula
One formula with four numbers that draws starfish, petals, shields and squares. Nested as a family, each ring a step further along, it blooms from spiky to round.
Cairo Tiling
Pentagons laid like paving, four ways round, two by two into hexagons. Slide the bar and the whole floor shifts from squares through equal-sided pentagons and back.
Ulam Spiral
Write the counting numbers round a spiral and dot the primes. Nobody has explained why, but they crowd onto diagonals and curves where there should be none.
Epicycles
Circles riding on circles. Two are a pair of planets: join Earth and Venus every few days for eight years and the lines open into a five-petalled rose.
Ouchi Illusion
A disc of upright bricks on a field of bricks lying flat. Let your eyes wander and the disc seems to float and slide on its own, though nothing on the page moves.
Shukhov Tower
A curved tower made entirely of straight lines. Two sets of lines lean opposite ways between rings, and the waist pulls in by itself, as in Shukhov's steel towers.
Loxodrome
Steer a ship on one fixed compass bearing and it spirals for ever towards the pole. Drawn by the dozen they wind a globe like a ball of string.
Maurer Rose
Hop round a rose curve in steps of the same angle and join the dots. One whole number for petals and one for the step make nets, stars and lace.
Asanoha
The Japanese hemp-leaf pattern: a grid of triangles with every centre joined to its corners. Drawn as wooden kumiko, it opens into pinwheels.
Spirolaterals
Walk one step, turn; two steps, turn; and so on up to n, then start again. Most walks come home, drawing knots and stars from one simple rule.
Chaos Game
Pick a corner at random and jump half way towards it, again and again. The dots never land anywhere near randomly: they draw the Sierpiński triangle.
Curve Stitching
Every thread is straight, and yet the curves appear. Join points along two arms, first to last, and the threads wrap a parabola; stitch a star and they bloom.
Polar Roses
Plot r = cos(kθ). Whole numbers give flowers of petals; fractions wind round and round into lace. Laid out as a table, n down and d across.
Hailstones
Halve it if it is even, triple it and add one if it is odd, until you reach 1. Grown backwards from 1, thousands of numbers become a coral; drawn as arcs, they rise and fall like hailstones.
Archimedean Tilings
Only eleven ways exist to tile a floor with regular polygons so that every corner looks the same. Each is named by the shapes round a corner: 4.8.8 is a square and two octagons.
Physarum
A slime mould has no brain, yet it builds efficient networks. Thousands of tiny agents follow each other's trails, and veins grow on their own.
Squared Squares
Cut a square into smaller squares. Let the sizes repeat and you have a patchwork quilt; make every one different and you have one of the hardest puzzles in geometry.
Stipple and Single Line
Thousands of dots, crowded where the picture is dark, nudge themselves apart until they settle like a hand-stippled print. Joined by one line that never crosses itself, they become a drawing in a single stroke.
Strange Attractors
Two lines of sines and cosines, applied to a point a few hundred thousand times. It never repeats, yet it keeps to one folded, smoky shape, and four numbers choose which.
Mod Tables
A times table where every answer is swapped for its remainder. Hatch each remainder at its own angle and the table weaves itself into a symmetric quilt.