🌀 Spirograph — Hypotrochoid & Epitrochoid Curves

Draw beautiful mathematical curves using spirograph equations. A small circle rolling inside or outside a fixed ring traces intricate symmetric patterns. Explore integer and fractional gear ratios.

Mode

Presets

Outer radius R = 120

Inner radius r = 30

Pen distance d = 30

Speed = 5

Stroke width = 2

Hue offset = 0°

Type: Hypotrochoid
Petals / symmetry: 4
Rotations to close: 4

x=(R−r)cos(θ)+d·cos((R−r)/r·θ)
y=(R−r)sin(θ)−d·sin((R−r)/r·θ)