Types of Fractals
WHAT ARE THEY?
Plasma fractals are perhaps the most useful fractals there are. Unlike most other fractals, they have a random element in them, which gives them Brownian self-similarity. To create a plasma fractal on a rectangular piece of plane, you do the following:
1. Randomly pick values for the corners of the rectangle.
2. Calculate the value for the center of the rectangle by taking the average of the corners and adding a random number multiplied by a preset roughness parameter.
3. Calculate the midpoints of the rectanglesí sides by taking averages of the two nearest corners and adding a random number multiplied by the roughness parameter.
4. You now have four smaller rectangles. Do steps 2-4 for each of them.
After calculating the values, you can draw the picture by coloring the points depending on their value. Below are two plasma fractals with a small and a large roughness value:
Due to their randomness, plasma fractals closely resemble nature. Because of this, you can use plasma fractals in many different applications. For example by using standard atlas colors and determining the heights by the values of the points, we can get very realistic landscapes:
These kinds of fractal landscapes were used for special effects in many movies, including Star Trek. By using other colors, we can get realistic pictures of clouds:
We can create equivalents of plasma fractals in 1 dimension by randomly choosing the endpoints and then calculating the midpoint using roughness. This allows us to create pictures like the one below:
|Landscape Applet - Creates randomly generated 3D landscapes based on plasma fractals. Allows use of two different coloring textures and change of roughness level.|
A basic explanation of plasma fractals and creation of 3D landscapes. Includes a small, but slow loading, gallery