Jacob Bernoulli · 1694 · lemniscus, a hanging ribbon
r² = a² cos 2θ
(x² + y²)² = 2c²(x² − y²)
Every point on the curve holds the same product of distances to the two
foci at (±c, 0), where c = a/√2. Riders move at constant
parameter speed, so they crawl at the lobe tips and whip through the node —
the colour of each rider is |dP/dt|.
A generative rendering of the lemniscate of Bernoulli, the curve of constant distance-product about two foci. Nested rotated copies interfere into a rosette while a feedback transform pulls the accumulated light into a receding spiral.