A formula, not a file
Every study is a pure function of a compact parameter object. There are no imported glyphs and no hand-authored path assets. The path commands are calculated from points every time the component renders.
Method / materials / motion
How the lines
come alive.
A small equation, sampled often, can behave like a living drawing. This collection uses one disciplined rendering system across one hundred different constructions, then leaves the consequential choices visible.
A note on math and making
Math does not remove ambiguity. It gives ambiguity structure.
A drawing can feel inevitable when the decisions behind it have disappeared. Parametric drawing reverses that illusion. It names what may change, holds some things constant, and makes every visible line the consequence of a choice.
There is no single correct state here. At t = 0, the system rests. At t = 1, it is fully disturbed. Between them is a continuum of valid forms. The drawing remains itself without remaining identical.
The calculation produces possibilities. Judgment decides which possibilities matter. That is where technical precision becomes a form of craft.
Read “Of Math and Men”One value disturbs the system
Hover and keyboard focus set a target of 1. Leaving sets a target of 0. An interruptible spring moves between them, so reversing midway remains continuous.
Geometry does the moving
No SVG group is translated, rotated, or scaled. Radius, phase, sample position, curvature, and local offsets change inside each equation. The drawing deforms instead of moving as one object.
The line stays constant
Every element is fill-free, round-capped, and drawn at the same 1.7 pixel stroke. Non-scaling strokes keep the visual weight stable at every display size.
The shared interface
drawIcon(params)
t ∈ [0, 1]
points = formula(t, shapeParams)
svg = points.map(drawStroke)The same contract can produce a circle field, a projected surface, or an iterated attractor. The family changes. The motion architecture does not. Naming the parameters makes the creative judgment inspectable, revisable, and available for someone else to use.
The mathematical index
Twenty-eight families, one visual grammar.
- 01Circle lattices
- 02Stepped cells
- 03Surfaces of revolution
- 04Lissajous figures
- 05Hypotrochoids
- 06Harmonic fields
- 07Polar roses
- 08Saddle meshes
- 09Phyllotaxis
- 10Strange attractors
- 11Möbius bands
- 12Torus knots
- 13Epicycloids
- 14Superformulas
- 15Fermat spirals
- 16Fourier ribbons
- 17Maurer roses
- 18Modular chord webs
- 19Truchet fields
- 20Tangent rings
- 21Loxodromes
- 22Klein sections
- 23Bessel waves
- 24Chebyshev bands
- 25Caustics
- 26Reuleaux systems
- 27Clifford maps
- 28Harmonic knots