Parametric curve / Study

Variable-frequency spirograph

Geometry

A three-term parametric curve with an adjustable frequency multiplier k, from 1.0 to 30.0 in steps of 0.1.

x(t) = 0.70·cos(t) + 0.35·cos(k·t) + d·cos(n·t)
y(t) = 0.70·sin(t) − 0.35·sin(k·t) + d·sin(n·t)

0 ≤ t ≤ 2π. Decimal values of k can leave the curve open. Here n is the loop count and d is the loop size.

Shape & appearance

Frequency multiplier k Loops n Loop size d Line width Base colour Auto-sweep first slider

Saved PNGs

PNG captures are named with their parameter values. Commit the downloaded files to the repo and they will appear here automatically (fetched via the GitHub API).