Mixed Spirograph

Drag the circle, the point on it, or the free probe — straight in the z plane.

The polynomial

Coefficients — drag them

—

Motion

radius r 1.000

angle θ 0.00π

plot out to

Gallery

z plane r = 1.000

angle 0.00π

probe —

ZERO HIT

w plane image of the circle

times round 0 0

closest approach to 0 —

P at probe —

Times round 0, against radius — click to set r

What you are looking at

Each term a z^mz̄ⁿ is drawn as one arm in the w plane, laid end to end. On the circle of radius r that arm has length |a|·r^m+n and turns m−n times while θ goes round once. The chain's endpoint traces the image curve.

m−n > 0, anticlockwise m−n < 0, clockwise m−n = 0, does not turn the circle, and 0 in the w plane the free probe