This archive contains fractal images that I generated with Fractint, mathematical and artistic notes on each, and resources for generating them yourself. Some images are 800x600 and others are 1024x768, depending basically on when I created them.
Images
A minibrot
The classic mandelbrot set is by far the most famous fractal of its type, mentioned in every book on fractals. It is based on iterating the formula zn+1=zn2+z0 on the complex plane, where z0 is the pixel coordinate, and colouring each pixel according to the number of iterations needed to make |z| greater than four. Among its features are an infinite number of minature copies of itself, often called "minibrots". This image is a fine specimen of such a minibrot.
A fractal alien
In this picture, I see a decidedly feminine fractal alien. I have used the image to decorate a wooden tray. Mathematically, it is an image from a classic Julia set. Every good book on fractals mentions Julia sets, and how for every point in and around the Mandelbrot set, there is a corresponding Julia set full of the characteristic geometry of that region. Whereas in the Mandelbrot set, the pixel value is added at each iteration, in a Julia set, a constant is added instead.
My fractal
Finding your own fractal-generating formula can be fun, as it gives you a world of infinite detail of your own. This one is based on the formula zn+1=(z0*log (zn+z0)) / (log(z0)) - (zn+z0) and there doesn't have to be a reason. The overall appearance is attractive and mysterious, I think, and I can just see it as a design for some sort of magical artifact.
It yields some interesting surprises when we zoom in. For example:
- An infinite flock of birds on the shoreline of chaos
- The Tower of Bubbles
- Something to do with balloon animals and seahorses
Sunshine in an egg
If, in some mythology, the sun were to hatch from an egg, the egg might look like this. Just as every point of the classic Mandelbrot set has its corresponding Julia set, so it is with fractals based on other formulas. This is an example of a "Julia" set corresponding to my fractal formula above.
Mandelbrot Ex Machina
This is the image I use for my computer desktop. I see an image of linear, mechanical shapes being grinded into chaos by a vaguely Mandelbrot-shaped cog. The formula is ultimately the same as in my fractal above, but it is used in a very different way.
Tilting my fractal
The colouring for the classic Mandelbrot Set is based on when the value of |z| exceeds four, because it can be shown that any value which does exceed four will continue to approach infinity. However, for my fractal formula, there is nothing special about the number four; it's really arbitrary. You can think of the fractal as a slice through a three-dimensional shape, in which the third dimension is the value which |z| must exceed. I experimented once to see what happens if the value |z| must exceed is equal to the real component of the pixel, which makes, if you like, a diagonal slice through that three-dimensional shape. This was a whimsical idea but it generated two very nice fractals.
- A fractal spider's web. It is, I think, sticky, with fragments of leaves stuck to it. But also stuck to the web are smaller webs, and stuck to those are smaller webs again. Truly a fractal spider's web.
- A psychadelic spiral. Intricate swirls within swirls, very pretty. I use a small portion of this image as part of my avatar, on various places on the Internet.
Battle of the Chistmas trees
This looks to me like two Christmas trees engaged in psychic warfare, draining vitality from each other. Unfortunately, I can't let you explore this fractal for yourself, as I have lost the information about the formula that generated it.
Source files
The following are supplied for people who have Fractint and would like to explore these fractals. You should instruct your browser to save these files to disk.
- Formula file
- Parameter file
- Four 256-colour palettes: (1), (2), (3), (4)
Notes:
In the parameter file, the item aaaaaaaa restores default parameters, which other items in the file may assume to have been reset. For this reason, you should select aaaaaaaa immediately before selecting another item in the file, or your selection may not display correctly. This is particularly important after viewing the Mandelbrot Ex Machina fractal, which changes several settings that only aaaaaaaa will change back.
Some fractals take a very long time to generate. The Tower of Bubbles is definitely an overnight job, for example.
The parameter file assumes 800x600 screen resolution. If you wish fractals to use 1064x768 resolution instead, change the bit in the entry aaaaaaaa that says video=sf6 to video=sf7.
DOS mode in modern versions of Windows is very buggy indeed, and Fractint won't run satisfactorily (except perhaps in very low screen resolutions). The emulator DOSBox runs Fractint more-or-less bug-free in 800x600 resolution as of version 0.65, but it is still buggy in higher resolutions.
