Fractals

Have you ever contemplated infinity? As a young boy I remember staring into the night sky and trying to comprehend “it never ends.” After all, if you came to a wall at the edge of the universe, what is on the other side of the wall? Mandelbrot fractals are like that. No matter how far you look into a fractal structure, there is always something next. And just like the artifacts of the cosmos, the beauty is astounding.

One of the simplest things you can do with the Mandelbrot set is search for Mandelbrot Midgets. I have been so astounded by the simplicity of their complexity that I started a book on the subject, mostly to help me catalog what I was finding. I was delighted when I found that others enjoyed my writings on the Midgets which prompted me to format the content of my explorations into book form.

Posted here is the first two chapters of that book in pdf format. It is 2.6 MB, so make sure you have a fast enough link (or enough time) to bring it down. Then, I’d be very interested in what you think.

Enjoy!

Chapters 1 and 2

This is a view on the way to the deepest Midget I’ve rendered (it will be in the book). It took over 86 hours for 8 cores (Core 2 Duo vintage) to render this image at 300 dpi. If you wonder what you are looking at — read the first chapter in the book above.

Magnification: 1.4097655E67

Note that the thumbnail links to an image that is just over 1MB.

Here is the rendering of the deepest Midget I’ve ever found. This image required over 225 hours for 8 cores to render at 300 dpi. Magnification is 6.1679441E71 being four orders of magnitude deeper from the image above (I thought I had found a Midget in that image but was disappointed after 86 hours of work to find that it was only a stop along the way).

Magnification is 6.1679441E71

Image size is 1.06 MB.