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Nature-inspired generative art

Forms with the feel of something grown. Sunflower spirals, ferns, coral, shells and soap-film surfaces sit beside attractors, harmonographs and circle packings, curves that nature and mathematics share.

Nature inspired

54
Spiral, archimedean spiral

Spiral

Turns · Arms · Spacing

Physarum, physarum polycephalum

Physarum

Start from · Food spots · Sensor angle

What each one draws

Pearl Lace

Circles reflected through circles become intricate necklaces. Quiet openings hold the composition while tiny pearls collect around their edges.

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.

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.

Azulejo Rosettes

Scalloped flowers and curved diamonds grow from a repeating ornamental field. Nested ink lines give each tile a delicately engraved rhythm.

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.

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.

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.

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.

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.

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.

Barnsley Fern

Four affine maps, chosen at random, iterate a point. The attractor is a fern: self-similar fronds from a handful of matrices.

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.

Fraser Spiral

Concentric circles built from leaning cords. Trace one with a finger and it closes; let go and it winds inward again.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.