Stability and chaos are analyzed by computing the Lyaponuv exponent which is plotted above.

A generalization of the Cornu spiral, this is an example of a polynomial spiral described by Dillen (1990) for which the curvature is a polynomial function of the arc length.

Klein's j-invariant in the complex plane

A plot of z = |W(x+iy)|, where W is the Lambert W function

Icosahedron by Richard Sweeney

Point collections by Zach Kron

Zach Kron writes an interesting post about this image, which is created by using several layers of a very basic shape repeated in a pattern and then varying the size and angles, and seems to show up a lot on ceilings and walls of buildings.

"Spiral waves in colonies of the mold Dictyostelium discoideum. These patterns are created when the mold forms aggregates in response to some external 'stress', such as a lack of moisture or nutrients." (BALL, 1994)

An interesting new look at the Menger sponge: slicing the sponge at an angle produces six-sided stars. One of the proposed exhibits for the Museum of Mathematics, MOMATH.