Is this how real marbling works?

It is the geometry of it. Real marblers float ink on a thickened bath and drag combs through it; the ideal-fluid formulas used here reproduce the displacement those actions cause without simulating the fluid, which is why the swirls are exact rather than approximate.

Who worked out the mathematics?

Aubrey Jaffer published the closed-form drop and tine displacements in the early 2000s under the name mathematical marbling, building on Lord Kelvin’s vortex formulas; later papers extended the same idea to wavy combs and curved tines.

Will this slow my computer down?

It is tuned to run smoothly on an ordinary laptop. If it feels heavy, raise the Pixel size or lower the speed in the settings; every control takes effect immediately.

Is the Paper Marbling screensaver free?

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

How do I exit the Paper Marbling screensaver?

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

Why don’t the inks mix in real marbling?

The pigments, mixed with a surfactant such as ox gall, are dropped onto a viscous liquid called size and float on its surface instead of dissolving into it.

What is the difference between suminagashi and ebru?

Suminagashi is the Japanese method of floating ink on plain water. Ebru is the Turkish name for marbling on a thickened bath (size), where combs, rakes and styluses shape the colours.

What is the bath made of?

Traditional size was made from gums such as gum tragacanth, guar or psyllium. Carrageenan became common later, and modern marblers also use sodium alginate or methylcellulose.

Paper Marbling Screensaver

Paper Marbling is a free, in-browser simulation of the marbler’s tray, done with mathematics rather than fluid dynamics. Every ink drop is a polygon; dropping a new one pushes every existing point outward by the exact formula for an incompressible fluid, and drawing a comb tooth through the bath shears the points along its line by a closed-form displacement. Drops fall and combs sweep on a slow schedule, and the bath keeps swirling. Nothing to download, and ESC exits at any time.

How the Paper Marbling screensaver works

Real marbling floats inks on a thickened bath, where they spread without mixing, and the marbler drags combs through them. Aubrey Jaffer noticed that both operations have exact solutions if the bath is treated as an ideal incompressible fluid, so a picture can be computed without simulating anything.

A drop of radius r at centre C moves every existing point P to C + (P − C)·√(1 + r²/|P − C|²): the ink already there is shoved outward by exactly the area the new drop occupies, and the new drop is added on top as a circle of 128 vertices.

A tine is a line through the bath with a direction; every point is displaced along that direction by α·λ/(d + λ), where d is its distance from the line. Points on the line move by α and the effect dies away over a scale λ. A comb is several parallel tines applied together, which drags the drops into the feathered chevrons of a nonpareil pattern.

The polygons are drawn oldest first, so later drops sit on top like inks do. A large base coat is laid down first so the paper is never bare, and the oldest drops are retired once a couple of hundred are on the tray.

Marbling, from Ebru to mathematics

Marbling is a craft with a long history. In Japan, suminagashi (“floating ink”) places colours on plain water, and a drop of surfactant-laden water pushes them into rings. In Turkey, ebru is the modern name for the size-based method, in which pigments mixed with a surfactant such as ox gall are dropped one after another onto a viscous liquid called size, traditionally made from gum tragacanth and later often from carrageenan.

Rakes, combs and styluses then draw the floating colours into more intricate designs: a stylus makes swirls, and a comb dragged across the tray makes regular, feathered patterns. Finally a sheet of paper is laid gently on the surface, the colours transfer to it, and it is lifted off and hung to dry. Each pour and stroke differs slightly, so each print does too.

The mathematical shortcut works because an ideal incompressible liquid has predictable motion, so the effects of drops and combs can be written down exactly. Real baths are viscous, and the real craft involves surface tension, ink chemistry and timing that the formula leaves out, so the digital picture shows the geometry and not the full craft.

A worked example

At the defaults — Speed 4, comb every 6 drops, Classic inks on cream paper — navy, oxblood, ochre and teal drops land every second or so, each pushing the earlier rings into flattened crescents around it, and every sixth beat a comb rakes across the tray and pulls the whole field into feathered arches. Switch to Indigo inks for a Suminagashi look, or Pastel for endpaper pinks and blues.

Settings & tips

Comb every 2 drops for a dense feathered pattern; every 20 for mostly concentric rings.
The paper colour shows through only where the base coat is pushed aside — try a dark paper with Pastel inks.
Speed 1 is close to the real pace of a marbler working a tray.

Frequently asked questions

Is this how real marbling works?: It is the geometry of it. Real marblers float ink on a thickened bath and drag combs through it; the ideal-fluid formulas used here reproduce the displacement those actions cause without simulating the fluid, which is why the swirls are exact rather than approximate.
Who worked out the mathematics?: Aubrey Jaffer published the closed-form drop and tine displacements in the early 2000s under the name mathematical marbling, building on Lord Kelvin’s vortex formulas; later papers extended the same idea to wavy combs and curved tines.
Will this slow my computer down?: It is tuned to run smoothly on an ordinary laptop. If it feels heavy, raise the Pixel size or lower the speed in the settings; every control takes effect immediately.
Is the Paper Marbling screensaver free?: Yes. It runs free in your browser with nothing to download or install, and it keeps working offline once the page has loaded.
How do I exit the Paper Marbling screensaver?: Press the ESC key at any time to leave fullscreen and return to the page.
Why don’t the inks mix in real marbling?: The pigments, mixed with a surfactant such as ox gall, are dropped onto a viscous liquid called size and float on its surface instead of dissolving into it.
What is the difference between suminagashi and ebru?: Suminagashi is the Japanese method of floating ink on plain water. Ebru is the Turkish name for marbling on a thickened bath (size), where combs, rakes and styluses shape the colours.
What is the bath made of?: Traditional size was made from gums such as gum tragacanth, guar or psyllium. Carrageenan became common later, and modern marblers also use sodium alginate or methylcellulose.

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