A point distribution is said to be fractal if it exhibits scale invariance. In other words, the distribution pattern looks the same at a range of different magnifications. The distribution of mineral deposits such as gold resulted from the favorable interaction of a number of controlling parameters including fracture patterns. There is no guarantee that such controls acted in the same way on all scales or originated as a result of the same tectonic process. However, if controls are related, e.g. to one generation of fractures, a fractal distribution of gold occurrences is expected within a certain scale range.

To test the fractal nature of a point distribution, square grids of various cell sizes are superimposed on the points. For each grid cell size (as characterized by the side length of a grid square), the number of grid squares required to cover all points is counted.

If the distribution pattern of the points is scale independent or fractal, it can be described with a fractal relationships of the type: N(r) = C r^D, where N(r) = the number of squares with side length 'r' required to cover all points, 'C' = a fractal constant and 'D' = the fractal dimension.

Plotting N(r) against 'r' on a log-log scale will result in a straight line with slope -D if the distribution is truly fractal. Slopes may also be kinked, with the kink point representing a characteristic dimension at which one geological process overtakes another in determining the distribution pattern of the points under investigation. Such a dimension may control the clustering behavior of the point distribution pattern.

DotProc's Fractal distribution plot window looks as follows:

The data can be saved as tab-delimited text files (or copied to clipboard) that can be opened in data management programs such as Excel, where the data can be analyzed further.

The chart can be zoomed by dragging the mouse selecting a zoom rectangle. To zoom all drag the mouse towards top-left.

Click on "Show / Stop" button or press "ESC" key to stop the operation.

The following attributes of the Orientation diagram can be changed by selecting "Tools / Settings" menu item: