Click here to see fractals in my Java applet.
Click here to download fractal wallpapers in .bmp format that tile seamlessly.
Another feature associated with fractals is infinite detail. Fractals are becoming famous for their intricate beauty.
Look at the leaf and compare it to a real Maple leaf. The similarity is amazing. Fractal geometry is considered by many to be the geometry of nature. Many other examples of fractals exist in nature, such as the branches of a tree, rough coastlines, and planets orbitting stars which are travelling around galaxies.
If you want to know more about fractals, I recommend the books Fractals Everywhere by Michael Barnsley and Chaos, the Making of a New Science by James Gleik.
x' = ax + by + e
y' = cx + dy + f
You can apply the same idea to get the following 3-D formulas:
x' = ax + by + cz + j
y' = dx + ey + fz + k
z' = gx + hy + iz + l
Each fractal has two or more sets of values for the constants (a, b, c, . . .). These equations allow you to shrink, stretch, rotate, flip, and slant the image to get each of the smaller images.
The computer starts with a point that it knows is in the fractal, then randomly picks one of the maps (sets of constants) and calculates a new point. It plots that point, then picks another map. It will keep going through this cycle until you stop it.
There is another number associated with each map that changes the probability that a computer will pick that map. If all maps were equally likely, the fractal would be lighter in larger maps and darker in smaller maps. Adjusting this number makes the fractal even. It can also be adjusted to make the fractal uneven; for example, a higher number makes the veins visible in the leaf and makes the squares different shades in the quilt.