Create mesmerizing geometric art with spirograph mathematics. Adjust the gears, pick a palette, and watch beautiful curves emerge.
How it works
A hypotrochoid is traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is at a distance d from the center of the inner circle.
x = (R−r)·cos(t) + d·cos((R−r)/r · t)
y = (R−r)·sin(t) − d·sin((R−r)/r · t)
Controls
Outer R (R) — Fixed outer circle radius
Inner r (r) — Rolling inner circle radius
Pen d (d) — Pen distance from inner circle center
Rotations — Number of rotations to trace
Line Width — Stroke thickness
Glow — Neon glow intensity
Tips
Try whole-number ratios of R/r for closed shapes
Golden ratio relationships create complex beautiful patterns