Strange attractor pattern generator

Order that never repeats itself. Choose a Clifford or De Jong attractor or a harmonograph, one of six parameter sets, how far the picture is zoomed and how rich the shading, and export a seamless pattern as SVG, PNG or CSS.

Open in the generator How it works

Curling orange and blue ink-like shapes like a pair of waves on a very dark navy ground, a Clifford attractor

Pictures drawn by a formula

An attractor is the set that a simple rule keeps visiting. The Clifford and De Jong maps take a point, apply two lines of sines and cosines to get the next point, and repeat. Run for half a million steps, the points draw delicate sheets and filaments that no one drew. A harmonograph is the same idea in a machine: two pendulums, one for each axis of a pen, that slowly lose energy, so that the line spirals inward as it draws.

Ornamatic uses well-known sets of parameters; the pictures are results of the formulas, and nothing else.

How the generator builds them

The points of the Clifford and De Jong maps are counted in a fine grid, folded into the tile by taking each coordinate modulo the tile, and shown as three nested bands of density. A zoom of 1 shows the whole attractor once, while a smaller zoom folds it over itself, so the sheets weave through each other and the tile joins up at every edge. The harmonograph draws one damped curve in every cell.

Because the fold is applied to the picture, the tile repeats without a seam for every zoom. The parameter set picks one of six maps or pendulum ratios.