033

Modular chords

Straight lines between points on a circle, and a curve that was never drawn.

Field

Detail

Study

033

Chapter

Number theory

Equation

(m × k) mod N

What moves

m, from 2 to 6; the chord index k

Structure

Film

Colour means

m, the multiplier

Straight lines between points on a circle, and a curve that was never drawn.

240 points sit on a circle. Each point k is joined to point 2k, counting round again past 240. Only straight lines are drawn, yet a heart-shaped curve appears where the chords brush past each other. Each chord touches that curve at one computed point, and those points are marked in violet. Stacked for m = 2 to 6, the rule builds a tower of curves, one per integer.

Each study takes one equation and lets the computed result move.