02/12/2008

Fractal Profile and Surface Generating Tool

This tool is for generating fractal profiles and surfaces.

FRACTAL PROFILES

The profiles are generated by the midpoint displacement method.

Saupe,D.    "Algorithms For Random Fractals", Ch 2, pp. 71-113.  in Peitgen, Heinz-Otto And Saupe, Dietmar, Ed.  "The Science of Fractal Images", Springer-Verlag, NY (1987).  QA 614.86/s417/1987 Method:  Midpoint displacement and succcessive random additions in 2 dimensions.

Other ref in same book: Voss, R.D., “Fractals in nature:  form charactrerization to simulation”.  Chap. 1 in THE SCIENCE OF FRACTAL IMAGES, H-O. Peitgen and D. Saupe eds., Springer-Verlay, NY. 1988.

•       1      random      fixed
•       2      regular     fixed
•       3      regular      variable
•       4      random      variable
For the variable D commands, inputs are the recursion level list, (0 0 0 0 0 0 0 0 0 0), and a fractal dimension list (1.5).

Here, there is only one D, with index 0, which is used at all recursion levels.  The number of indices in the recursion level list determines the number of levels, and thus the number of points in the profile.

Here:

(0 0 0 0 0 1 1 1 1 1) and (1.2 1.8)

yields a curve that has D = 1.2 for the first recursion levels - the larger length scales, and D = 1.8 for the latter recursion levels - smaller length scales.

(1 1 1 1 1 0 0 0 0 0) and (1.8 1.2) yields the identical curve.

### Fractal Surfaces

The fractal surfaces here are two-dimensional arrays (width, length) where the pixel value represents height -  this surface has the given fractal dimension.  The surfaces are shown below as images, where the pixel value represents intensity.

The Surfaces button gives these options:  .  The default parameters give these images:

 2D 1D + Translation 1D + 1D

The 2D surface, with the "regular" option, looks like this: