Ian Sammis

The image of an endless braided cord can be represented as a function $f:\mathbb{R}_2\to\mathbb{R}_3$ from a location to an RGB value by finding the nearest point on each strand, shading each point within some thickness $T$ of a strand with a brightness that drops to zero at distance $T$ linearly, then writing rules to handle overlaps. This gives us an endless braid that can easily be composed with other maps. Composing with the conformal map $g(z)=z^2/2$ creates four braids in the $\frac{N\pi}{2}+\frac{\pi}{4}$ directions. Cropping this we arrive at a unit cell that can create a diagonal braided net throughout the plane. The displayed movie is that braided net mapped through $\frac{1}{z^\alpha}$ for steadily increasnig values of $\alpha$.