I just finished watching "Between the Folds," a documentary on origami and paper folding by Vanessa Gould, and was blown away by some of the amazing works and artists in the film. One of my favorites was Chris Palmer, whose works are about movement and light.

This video is inspired by some of his other pieces:

An image from an awesome demo by Ed Pegg Jr. that's part of the Wolfram Demonstrations Project. This image corresponds to Gaussian integers raised to the 11th power. The demo allows one to view Gaussian integers raised to any fractional power. The user can choose a numerator and denominator less than 20.

Gaussian integers raised to the 17/6 th power

Voronoi Patterns by Craig S Kaplan

Algorithmic art created by a program called LORMALIZED by Reza Ali that uses the Lorenz equation.

This image by Gabriel Doyle is a representation of the universal cover of the doubly-pointed Heegaard diagram of genus 1 of a (1,1)-knot.

"Octopod" by Syntopia (Mikael Hvidtfeldt Christensen) is an example of algorithmic art.
"In algorithmic art the creative design is the result of an algorithmic process, usually using a random or pseudo-random process to produce variability."

A Lorenz attractor by Nathan Selikoff, titled "Butterfly Effect."

"Equal Areas" by Susan McBurney.
This image, inspired by Leonardo DaVinci, builds upon a concept of equal areas. The sum of the areas of the red shapes in the bordering semicircles is equal to the sum of the areas of the red shapes inside the center circle; and the same goes for the green, yellow, pink, and peach shapes.

"Knot Structured" by George W. Hart was made by assembling 30 identical pieces of laser-cut wood. Read more here.