New Software

Some more recent software that uses modern interactive design and accelerated graphics to allow exploration of the Mandelbrot and Julia sets in real time can be accessed below. To find out more click below to view the instructions.

If you have Java installed, you can download and run the software by clicking the button below. The downloaded file will unzip to a folder called JMsoftware, with three sub-folders containing the executable jar file, the Java source code and the license.

To run the program you may only need to double click on the jar file, or you should be able to start the program by right clicking the jar file, select "open with" and the "Java". The program can be shut down by closing any of the three windows.

The images below were produced using the software that goes with the Open University course M835, Fractal Geometry. Just click on an image to view a larger version, plus explanation. The set book for the course is 'FRACTAL GEOMETRY Mathematical Foundations and Applications' by Kenneth Falconer.

A Barnsley fern

Part of a Julia set

Scenery drawn from fractals

A logistic plot

A Newton basin

An IFS plot of a leaf

The Mandelbrot set

A self-similar subset of Mandelbrot

A plot of the mini-Mandelbrot on the needle

A Julia set of z² + c taking c from a self-similar subset of the Mandelbrot set

Generators

The two fractal curves below are constructed from a generator. At each stage in construction, every straight line is replaced by a scaled down copy of the generator that is the same length as the line it replaces. Theoretically, this process continues ad infinitum, but when drawing real images one reaches a point where smaller detail cannot be drawn.

Select the stage 1 option to see the generator, or the animation to see the construction.