Parametric curve / Study

Variable-frequency spirograph

Geometry

Adjust the amplitudes A and B independently, alongside frequency k, loop count n, and loop size d.

x(t) = A·cos(t) + B·cos(k·t) + d·cos(n·t)
y(t) = A·sin(t) − B·sin(k·t) + d·sin(n·t)

0 ≤ t ≤ 2π. Decimal values of k can leave the curve open.

Shape & appearance

Frequency multiplier k Primary amplitude A (originally 0.70) Secondary amplitude B (originally 0.35) 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).