Richard G Krutchkoff


Fractals are pictures generated by mathematical equations using an iterative plotting process. Some Fractals are exhibited in the complex plane and others are in the usual two dimensional plane. Fractals often exhibit self-similarity, which means, if you magnify a small piece of the picture you will find a picture looking like the original. If the resolution was high enough you could keep repeating this, forever, and still see a picture similar to the original. The small pictures in this file are both catalog pictures and links to high resolution copies of the Fractals exhibited (8.5X11 inches at 600 dots/inch). If you click on a link you will see a larger copy of the Fractal which you can right click on and copy. (If you click again the picture will become too large to see.) The larger picture may have a different orientation depending how I felt when adding the picture. It may not look like 11x8.5 or 8.5x11 but it will print properly. The Iterative function System fractals are usually 8.5x8.5 unless the width had to be made wider to fit the fractal. If you need to contact me to obtain a printed copy of the Fractal make note of the catalog number and your preferred orientation.

For a lecture on FRACTALS CLICK HERE.


These are Composite Fractals made up of one or more fractals superimposed on one another.


These fractals are obtained by using a number of pairs (at most 100) of affine [they donít send thing to infinity] linear equations. Each pair of equations takes a point and obtains another point putting a dot at that point in the color assigned to the pair of equations. A starting point, usually (0,0), begins the plotting system, which could go on forever, but is usually stopped after 10 million points are plotted. Most of these plots exhibit clear self-similarity, while in others it is not so clear. I have always believed that Iterative Function Systems were the mathematics of genetics.



The L and N series are Iterative Function System Fractals. If you want to use these in constructing words or the like, feel free to crop, resize and change the colors as needed.


3D Fractals are really just sculptures made from parts of fractals. I have several of these but some would be difficult to duplicate.


A One unit 3D flower fractal looks like figure A. It can be hung on a pin or placed on a table and rotated. Since the colors are hard to distinguish, only one of the layers are shown here.
Figure C indicates the color sections, backgroung (a), leaf sections (b,c,d). If none of the existing flowers appeals to you CLICK HERE. for a color chooser and find your own colors. Send me the 3 numbers, Red, Green, and Blue associated with each of a,b,c and d.


These may look like fractals but are actually polar coordinate graphs of equations. The numbers ending in an F can be made into flowers like those above.
For each of the flowers, or for the 2D graphs, I can create a copy with any colors you want. CLICK HERE. for a color chooser and find your own colors. Send me the 3 numbers, Red, Green, and Blue associated with each of the colors you want to replace.


The rest are some miscellanious stuff I made for special purposes.