While creating this website, we had a great deal of programming to do for the applets and many of the diagrams. Below are some of our own suggestions for programming fractals, which we came up with while doing it. Although some of the things here will be obvious to anyone who ever programmed, they are especially relevant to fractals.

AVOID REDRAWING

Letting your program redraw parts of the fractal has three major negative effects. First of all, it takes time without producing any image. Second of all, if your program is intended to be used by other people, to them it will look as though the program hung, since they cannot know that calculation is taking place meanwhile. Lastly, because of rounding errors that computers make when doing many calculations, the redrawn image will often be misplaced from the original one, producing an unclear image.

There are several thing you can do about this problem. One of them is making the program check if the current part of the fractal was drawn already. This is especially efficient in strange attractors. For Julia Sets, you can use the MIIM instead of the IIM to implement this method. Another thing, which can be done for base-motif fractals is designing the motif so that no parts of the fractal overlap. For example, for the Sierpinski Triangle, you can substitute the motif on the left with the one of the right.

This will not change the fractal, since the base is a triangle and the two segments that were cut out will be drawn by the other two sides anyway:

AVOID ITERATION

Although iteration is essential in fractals, it has a lot of negative effects. First of all, the time it takes to draw the fractal often increases exponentially with the number of iterations. Second of all, when the number of iterations becomes too large, the image becomes blurred because of the limit on resolution. Try to make the number of iterations as large as possible, but don’t overdo it. Remember, very often less is more!

GO FOR COLOR MAPS!

Color maps are capable of creating amazing thing for most fractals, such as 3D effects and a natural look. Further, what is even more important is that changing a color map in your program does not effect its speed or efficiency. It is obviously a good idea to take advantage of this.

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