Spirograph

Draws a hypotrochoid: the geometric curve you get from rolling one circle inside another with a pen offset from the center. The N/D ratio between the outer and inner radii sets how the loops nest. Think of it as the digital version of the toy.

Inputs

Outputs

Ideas

• Set N=5, D=3 for a classic five-loop star. N=7, D=4 produces a tighter weave with more crossings.
• Animate D with a slow Phasor so the curve continually morphs between forms.
• Feed into Colorize with Hue driven by Phasor for a constantly shifting hypnotic pattern.

Tips

• The curve closes after loops = D / gcd(N, D) revolutions. Coprime N and D give the longest, most intricate curves.
• N=D is invalid (the inner circle equals the outer). The node clamps D to stay below N.

Related

• Rosette: petal-and-weave variation
• Rose: simpler rhodonea curve
• Spiral: open inward-to-outward path