Some incredible renders of the Buddhabrot and Nebulabrot

I'm working on implementing buddhabrot/nebulabrot rendering in the Mandelbrot Explorer application. The buddhabrot - so named because it resembles the classic statue of Buddha - is a more beautiful version of the Mandelbrot, and the Nebulabrot is a slight variation on this.

The idea is that regions that escape the Mandelbrot set are plotted as they head off to infinity. The colour of each point depends on how often that point is seen to head off to infinity. Here are a few images - I can't wait to get a working demo - it does run very slowly in flash at the moment so I'll try and sort that out. Click on the images to expand them!

The nebulabrot uses a rendering Method that is exactly the same as the way false colour is applied to images of the universe by astrophysicists. The resemblance is phenomenal!

Enjoy them and I'll post a flash generator soon!

(Images are: Buddhabrot, Anti-buddhabrot, Nebulabrot, Nebulabrot horizontal)

The Julia Set

If you look at the Mandelbrot Explorer application in my previous post you'll notice a "generate julia set" button on the screenshots.

It turns out that each point on the Mandelbrot Set has an associated Julia Set. The flash app below moves around the complex plane, in a spiralling motion drawing the Julia Sets for each complex location. Just click the image to launch it!

Mandelbrot Explorer

As I've mentioned a few times now I've been working on an application for Windows called "Mandelbrot Explorer". Nothing special, just functional exploration of the mandelbrot and julia sets. This is what 3rd year physicists spend their time doing - a lot of C++!

Here are a few screen shots and an outputted jPeg file. The program is capable of producing high resolution "deep zoom" images of 1200 by 800 pixels. These can look amazing. It handles powers of the mandelbrot set, as well as different forms - including the amazing "Burning Ship" fractal.

Here are a few screenshots.

The classic Mandelbrot Cardiods

The burning ship fractal:

A high res output saved as a low quality jpeg

The Program is free of charge to anyone who wants it. Just send me a note and I'll provide download links! Enjoy the beauty of mathematics.