What is the deeper mathematical basis of our natural world? Throughout nature and technology – and places where they overlap – there are algorithmic systems that generate beauty. They appear in countless and surprising places: music, art, seashells, flowers, chemical reactions, and mathematics itself. They appear accidentally and intentionally in the arts and artifacts, from the beginning of human creativity. This presentation will be a survey of the designs & animations created by these systems, and a discussion of the code used in their creation.