Create mesmerising parametric curves by rolling circles inside or outside other circles. Adjust gear radii to produce hypotrochoid and epitrochoid patterns — the mathematical art of the classic Spirograph toy.
A point on a rolling circle traces a roulette curve. The ratio of the radii determines the number of cusps and the symmetry of the pattern.
Adjust the outer radius, inner radius and pen position. Watch the pattern build up as the gears rotate. Change colours for multicoloured designs.
The Spirograph toy was invented by Denys Fisher in 1965 and sold 50 million sets worldwide. The underlying mathematics — epicyclic gearing — was studied by ancient Greek astronomers to model planetary motion.