Pi everywhere.............circles...........spirals............the curved............pi is a ratio of a curved line to a straight one.......

Mandelbrot animation based on a static number of iterations per pixel

Mandelbrot set detail

The Mandelbrot set is the set of complex numbers ${\displaystyle c}$ for which the function ${\displaystyle f_{c}(z)=z^{2}+c}$ does not diverge when iterated from ${\displaystyle z=0}$, i.e., for which the sequence ${\displaystyle f_{c}(0)}$, ${\displaystyle f_{c}(f_{c}(0))}$, etc., remains bounded in absolute value.

A zoom sequence illustrating the set of complex numbers termed the Mandelbrot set.