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Wave and ripple patterns

Waves meeting, reflecting and standing still. These patterns draw interference fringes, Chladni figures, moiré and ripple fields as fine line work, from the physics of sound and light to simple sums of sines.

Waves & ripples

40
Moiré, moiré pattern

Moiré

Lattice · Density · Layer rotation

Spiral, archimedean spiral

Spiral

Turns · Arms · Spacing

Magic Angle, moiré pattern

Magic Angle

Twist angle · Lattice · Superlattice cells

What each one draws

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.

Lissajous Weave

Interlocking harmonic traces form a floating woven knot. Small phase offsets create depth and ribbons of negative space.

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.

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.

Harmonic Shells

A spherical harmonic pushes a sphere into lobes. Latitude contours describe its surface like topographic lines wrapped around a 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.

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.

Interference

Two radial waves meet. Their amplitudes add; lines trace equal values of the combined field. Move either source to reshape the drawing.

Sine Waves

Layered harmonics form a rippling sheet. Phase offsets pull parallel strands into luminous folds and open pockets of negative space.

Spiral

Archimedean arms: radius grows linearly with angle. Turns wind the coil; arms is how many start equally around the origin.

Ripples

Concentric rings from one or more sources. Wavelength is the gap between crests; sources scatter from the seed.

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.

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.

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.

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.

Sunburst

Wedges from a point, every other one inked. Straight edges throughout, and the field will not stay flat.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.