Marbling

This page covers paper marbling in closed form. A Marbling bath holds colored ink regions as vector outlines. drop floats a new circle of ink and pushes everything already floating aside. Four raking tools bend every region at once: tine, comb, a circular tine, and swirl.

Each operation is an exact point transform from the classic marbling equations, the area-preserving drop and the stylus family with exponential falloff. Regions therefore deform without ever tearing or crossing. The finished paper is ordinary geometry, so you can fill it with drawMarbling, stroke the outlines, or send them to SVG/PDF export as plotter-ready paths.

Contents

• The bath
• Dropping ink
• Raking tools
• Drawing and exporting
• Practical notes

The bath

var bath = Marbling()                 // spacing: 4 by default
var fine = Marbling(spacing: 2)      // smoother, heavier outlines

Marbling is a value type. Operations mutate it in place, so a copied bath is a snapshot, and you can rake that copy separately. spacing is the refinement grain. As a transform stretches an outline, its segments subdivide until none is longer than about that distance. The new points land exactly on the transformed curve. inks is the ordered stack, oldest first, and each MarbledInk(shape:color:) in it carries a fillable shape and its color.

var bath = Marbling()
for i in 0 ..< 20 {
    bath.drop(at: center, radius: 200 - Double(i) * 9,
              color: i.isMultiple(of: 2) ? navy : cream)
}
bath.comb(through: center, direction: .unitY, spacing: 90, strength: 260)
drawMarbling(bath)

Dropping ink

bath.drop(at: Vector2(400, 300), radius: 80, color: .indigo)
bath.drop(400, 300, radius: 80, color: .indigo)   // positional form

A drop pushes every floating point radially away from its center. A point at distance d lands at √(d² + r²), which is the displacement that preserves the area of everything around the drop. Earlier regions therefore thin into crescents, but they never vanish. Concentric drops of alternating color build the bull's-eye that every classic pattern starts from, and scattered drops make "stones."

bath.add(shape, color: .black)      // float an arbitrary outline as ink
bath.add(contour, color: .black)

add floats any outline onto the bath as it is, because only a drop displaces what is already floating. Every later tool then rakes that outline like any other ink. The classic move is to float text outlines and comb them, and a Shape keeps its holes, so glyph counters survive.

Raking tools

bath.tine(through: point, direction: pull, strength: 120, falloff: 48)
bath.comb(through: point, direction: .unitY, spacing: 110, strength: 260, falloff: 30)
bath.tine(around: center, radius: 200, strength: 300, falloff: 48)
bath.swirl(at: center, strength: 400, falloff: 96)

All four tools share one falloff law. A point at distance d from the tool moves by strength · 2^(−d/falloff), always parallel to the tool's motion. strength is the full displacement at the tool itself. For the two rotational tools that displacement is an arc length, so a negative value reverses the spin. falloff is the distance at which the pull halves.

• tine(through:direction:) pulls one stylus along a line. This is the stroke that drags a bull's-eye into a heart.
• comb(through:direction:spacing:) pulls a whole row of parallel teeth, one every spacing. Rows of drops under a comb become the feathered nonpareil. Keep falloff well under the tooth spacing, or the teeth blur into one broad shear.
• tine(around:radius:) drags the stylus around a circle, so everything near the track slides along it.
• swirl(at:) stirs a vortex. The middle turns hardest and the spin falls off outward, which gives the tight curl of French-curl papers.

Drawing and exporting

noStroke()
drawMarbling(bath)          // fills each ink in its own color, oldest first

drawMarbling honors the current stroke state on every outline, and it restores the fill afterward. Leave the stroke off for flat marbled paper, because a hairline stroke reads as engraved veining. For anything else, walk bath.inks yourself. Each ink's shape fills, strokes, clips, and exports like any other shape. The whole bath is vector geometry, so --export-svg and --export-pdf write true paths. A hatching pass then turns the fills into plotter line work.

Practical notes

• Deterministic by construction. There is no randomness inside the bath, so the same operations always marble the same paper. Randomize drop positions and colors with the sketch's seeded random, and the whole sheet then reproduces from its seed.
• Setup-shaped work. Outlines gain points as they stretch, so the cost grows with the number of operations. Compose the bath in setup(), or once per interaction, and redraw the result you kept. Don't rebuild the bath every frame.
• Order is the picture. Later drops sit above earlier ones. drawMarbling paints oldest first, so the stack reads in the order you poured it. A drop in the paper color carves negative space.
• spacing is the fidelity parameter. Halving it roughly doubles the number of points, and the default holds up over a full-canvas sheet. For long runs of one comb after another, try spacing: 6 while you sketch, then tighten it for the final export.
• True ink dispersion is a different tool. The bath is the classical kinematic model, which transforms outlines. Bleeding, granulation, and wet-into-wet diffusion need a simulation, so they are outside what marbling does.

Related: Watercolor (the painterly sibling), Text (outlines to float), Export (SVG/PDF and hatching), Variations (seeds that name a sheet).