Math and Art : Form As Mathematical Order
Math and Art
The eye is infinitely perceptive and complex. Between brain and eye, millions of judgments and organizations of thought occur without us being conscious of them, but when a composition feels balanced, when a spiral feels inevitable, when a pattern feels alive, it is because of a known organization exists, defined yet below the surface of definition.
Our unthinking perceptions are written in geometry, in proportion, in ratio; we are drawn to a world of order.
The tools below let you generate and examine those structures directly, and see what the eye already knew.
Nature Sequence
A sunflower and a branching river follow the same sequence. Patterns are everywhere.
Recursion
A shape that contains itself, at every measure, infinite to complex scale.
Repetition
Explore tessellation and create with symmetry and rotation.
Fractal Explorer
Zoom into the boundary between order and chaos, never-ending.
Children’s Fractal
Explore five types of fractals and make cut out fractal art arrangements.
Fractal Art Tool
Select from 22 fractals, cut out shapes and embellish on a canvas.
Kobayashi
Arrange blocks by color, shape and size according to Fibonacci arrangement.
Poly Art
Explore a world reduced to triangles, every shape defined by geometry.
Voronoi Diagram
Every region belongs to its nearest point — and every edge is halfway.
Labyrinth
Wander of the Labyrinth and Maze Studio Tool, create mazes and solve.
Truchet Tiles
Create with Truchet tiles: take one tile, arrange it in two orientations, and place it in a pattern.
Boids Algorithm
Murmuration
A murmuration of starlings, a school of fish, amazing. They form aerial shapes in the air or water, almost as if the flock has a group mind. But it is not as complex as that, it all comes down to math algorithm called Boids Algorithm. The tool we have above follows the 1986 work of Craig Reynolds, who wanted to know why flocks moved the way they did.
Research shows that birds in a murmuration or fish in a school have no group leader. Each animal is concerned only with how its immediate neighbors are moving, and they follow three rules: don’t crowd your neighbor, move in the direction they’re moving, and drift toward the center. Those are the entire instructions.
No one teaches birds or fish to flock. It is simply what happens when you apply a handful of mathematical rules to individual movement, and watch what emerges. It helps you avoid getting eaten as well.
The tool above mimics a school of fish or a flock of birds. The sliders control separation distance, alignment strength, cohesion, speed, and trail length. To simulate disruptions, click or tap anywhere and watch them regroup.