On October 19, 1939, the Centre national de la recherche scientifique was born. With((((x+1)²+(y+1)²-1)²-1/2+2*z²+1/2*(y+1)²))*

((((x+1)²+(y-1)²-1)²-1/2+2*z²+1/2*(y-1)²))*

((((x-3/2)²+(y/2)²-1)²-1/2+2*z²+1/2*(y/2)²))-1

we congratulate CRNS for its 80th birthday!
The formula gives a surface consisting of all points (x,y,z) where it equals 0.
You can modify it or tweak its parameters to change its shape.

The formula(x²+y²-1)generates a tube. By squaring it and adding some quadratic correction term(x²+y²-1)²-1/2+2*z², the formula can be converted to a torus. This formula is our building block. Substitution of the variables transforms and stretches the torus. A product becomes zero if any factor becomes zero. With this, we can construct unions. By multiplying more of such formulas, the union of the original shapes can be generated. With some further deformations, the equation for the formula above has been generated.

To continue exploring mathematical equations that create other wild, powerful, inspiring, provocative, sweet, curious, confusing, sometimes scary but always amazing three dimensional surfaces you can download SURFER, a desktop application for Windows, Mac or Linux.

This site was created by IMAGINARY, a travelling exhibition that shows mathematics can be beautiful, interactive, something you can touch, or a way to express your emotions beyond what words can achieve. It has visited over 55 countries since 2007.

Raycaster by Aaron Montag.

Created using
CindyJS
by Jürgen Richter-Gebert.