Mathematical images

A Julia set maps how a particular nonlinear dynamical system behaves.

The links below are to Julia sets of various iterators.

Using
Newton's Method on z^7 - 1

Using
Newton's Method on z^7 + z / 1000 - 1

Using
Newton's Method on z^6 - 1

Newton's method on three slightly assymmetrical roots

Newton's method on very asymmetric roots

Newton's method on seven slightly asymmetrical roots

Zoom-in of previous picture

Zoom-in of previous zoom-in

Newton's method on z^7 + i*z/100000 - 1

Julia set of z^3 - i*z + 1/4

Julia set of z*sin(z) + 1/5

Julia set of z * (1 + (z - exp(1.4*i)) / 2)

previous picture zoomed-in (This is a much bigger version of the little blue picture at the top of the screen.)

The link below goes to a picture of a tiny fraction of the Mandelbrot set, which maps the properties of Julia set of the iterator z -> z^2 + c.

Zooming
In on the Mandelbrot Set

I produced these images back in the day using a Windows application that I wrote in VB6(!).