12/12/2003

The images available here are of fractals similar to the von Koch Triadic Island.
Each series of fractal images is drawn using a minimum edge length appropriate for each series. The minimum edge lengths are usually 4, 6, or 8 pixels. The edge length determines the number of steps used to construct that particular portion of the fractal, and thus the fineness of detail. The minimum edge length corresponds roughly to the minimum step size that can be used in measuring the boundary fractal dimension, Db. The upper limit of the step size for valid Db measurements seems to be on the order of a tenth of the diameter of the fractal (see series4 plot).
I made the images using Lispix. Lispix also measures boundary fractal dimension.
The images are for testing image processing software that measures the boundary fractal dimension, Db, of particles or other objects.
von Koch Triadic IslandDb for this fractal is 1.262... a. Island outline as drawn with edge length of 4 pixels. b. Image of outline. (192x200 pixels) c. Filled outline. 
Construction of a von Koch Fractal
(Stoyan & Stoyan '94)


This chart shows the ranges of Db and a that result in drawable fractals. Colors  show minimum edge length (in pixels) where image is faithful to the fractal *. Small numbers in white boxes show parameters for a single image in a given series. Most series of images are confined to the regions of edge length 2  8 pixels (the blue  pink  yellow  white regions). The gray area represents nonphysical particles because drawing overlaps itself, except for very coarse renderings with very large minimum edge lengths  these can hardly be called fractals.
* Tested on fractals of 300  1000 pixels diameter. Minimum step length for which the perimeter of the fractal image is within 5% of the length of the drawn fractal. 
