What is the de Jong attractor?

A strange attractor produced by iterating a simple two-variable map built from sines and cosines, introduced by Peter de Jong. Depending on its four constants it draws an enormous family of folded, lace-like shapes, and it is a favourite of generative artists for that reason.

Why are dots used instead of lines?

Because the map jumps: each iteration lands far from the last, so a line between consecutive points would cross the whole shape and hide it. Plotting only the points lets the structure emerge from density, which is how the attractor is meant to be seen.

Is the de Jong Points screensaver free?

Yes. It runs free in your browser with nothing to download or install, and it works offline once the page has loaded.

What does the Seed setting do?

Everything is deterministic from the seed: the noise table, where the field’s features land and the order particles spawn in. Leave it blank for a fresh random layout on every run, or type any short word or number to get the same layout back each time.

How do I exit the de Jong Points screensaver?

Press the ESC key at any time to leave fullscreen and return to the page.

Why does the picture always stay in a square?

Each coordinate is a sine minus a cosine, each between minus one and one, so every value is between minus two and two.

Why do some parameter sets give nothing interesting?

The map may settle at a single point or a short loop, which looks like one dot or a few lines. Only chaotic parameter sets keep wandering across a rich shape.

How is this different from the Lorenz system?

Here the system takes discrete jumps from one point to the next, while the Lorenz system is continuous and evolves smoothly with time.

de Jong Points Screensaver

de Jong Points is a free, in-browser screensaver that iterates the Peter de Jong map with thousands of particles at once. Successive points of this map jump rather than flow, so instead of segments the saver lays down accumulated dots, and the attractor’s folded lacework builds up purely from where the points land most often. Parameters are drawn from known-good sets, and the orbit is probed at start-up to fit the screen. Nothing to download, and ESC exits at any time.

How the de Jong Points screensaver works

The de Jong map takes a point (x, y) and returns (sin(a·y) − cos(b·x), sin(c·x) − cos(d·y)). For the right constants a, b, c, d, repeating it forever never settles and never repeats, but the points all fall on an intricate folded shape — a strange attractor.

Consecutive points on this attractor are far apart, so joining them with lines would draw spaghetti. The saver therefore switches to points mode: every particle carries its own (x, y), iterates the map once per frame, and plots a single dot. Density is the whole image; where the map visits often the dots pile up and glow.

Random constants usually collapse to a point or a loop, so the four parameters are chosen from a list of known-good sets and jittered slightly by the seed. Because each set lands somewhere different and is not centred on the origin, the orbit is run for a few thousand steps before drawing and its bounding box is fitted to the canvas.

Each new particle is burned in for a couple of dozen iterations so it is already on the attractor before it plots. The stroke alpha is halved relative to other fields, and the default trail is 100 — a cumulative painting — because the shape only appears once enough points have landed.

Four numbers, endless pictures

The de Jong maps are named for Peter de Jong, and they reached a wide audience through the July 1987 Computer Recreations column in Scientific American by A. K. Dewdney. Paul Bourke later published many images and the equations on his website, and Clifford Pickover’s 1995 collection The Pattern Book includes high-resolution examples. In all of them, a pair of simple trigonometric formulas is iterated again and again.

Each new coordinate is a sum of two bounded terms, a sine and a cosine, so every point stays inside a square of side four around the origin. That bound is why the pictures fit on screen without any scaling tricks. Inside the box, the folding action of the sines and cosines stretches and tucks the points into delicate webs and veils.

Most sets of the four numbers do not give attractive results. Many fall to a fixed point, a short cycle or a faint smear, while a minority give chaotic shapes that fill out into pictures. Finding good ones is exploration: nobody can look at four numbers and predict the image, which is what makes the search for good constants rewarding.

A worked example

At the defaults — Blueprint palette, 2200 particles, Trail 100 — white and pale blue dots fall onto a dark blue ground and within seconds resolve into an intricate folded veil, densest along its creases. Type the seed 9k2x for the studio’s Blueprint orbit parameter set. Drop Trail to 60 and the veil keeps fading and re-forming, showing where the map is visiting right now.

Settings & tips

Leave Trail at 100: the attractor is a density picture and needs the points to accumulate.
Reseed to pick a different known-good parameter set; each is a completely different shape.
Monochrome on this field looks like a silver-gelatin print; Sakura like a pressed flower.

Frequently asked questions

What is the de Jong attractor?: A strange attractor produced by iterating a simple two-variable map built from sines and cosines, introduced by Peter de Jong. Depending on its four constants it draws an enormous family of folded, lace-like shapes, and it is a favourite of generative artists for that reason.
Why are dots used instead of lines?: Because the map jumps: each iteration lands far from the last, so a line between consecutive points would cross the whole shape and hide it. Plotting only the points lets the structure emerge from density, which is how the attractor is meant to be seen.
Is the de Jong Points screensaver free?: Yes. It runs free in your browser with nothing to download or install, and it works offline once the page has loaded.
What does the Seed setting do?: Everything is deterministic from the seed: the noise table, where the field’s features land and the order particles spawn in. Leave it blank for a fresh random layout on every run, or type any short word or number to get the same layout back each time.
How do I exit the de Jong Points screensaver?: Press the ESC key at any time to leave fullscreen and return to the page.
Why does the picture always stay in a square?: Each coordinate is a sine minus a cosine, each between minus one and one, so every value is between minus two and two.
Why do some parameter sets give nothing interesting?: The map may settle at a single point or a short loop, which looks like one dot or a few lines. Only chaotic parameter sets keep wandering across a rich shape.
How is this different from the Lorenz system?: Here the system takes discrete jumps from one point to the next, while the Lorenz system is continuous and evolves smoothly with time.

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