Euler

The Euler gallery of images explores various recurrence relations trapped by circles and rings. Named for Leonhard Euler, Swiss mathematician in the 1700’s, famous for forming the identity $e^{i\pi} = -1$, which has been called “the most beautiful mathematical formula ever”.

Euler #3

Euler 3 involves orbit traps of a ring and three lines perpindicular to the real and imaginary axes. Each image is a different view of the same fractal.

Euler #4

Recurrence relation $z_{n+1} = z_0 + sin(z_n^2)$ trapped by two rings.

Euler #8 and #9

Leonhard Euler developed the Gamma function, which is used in the recurrence relation for #8 and #9.