PUBLIC DOMAIN. The author has disclosed the algorithm and many of its properties on the web begining in late 2010 and it is his view that this constitutes "public disclosure". He repeated this position to the audience at ISAMA 11.
John is not on Facebook, does not tweet, has no cell phone, and doesn't use You Tube. THIS SITE is his internet presence. He does receive Email (see bottom of this page), answers his telephone, and opens snail mail.
For Powerpoint "movies" of the algorithm for different shapes click here. This is one of the best ways to really see what is going on.
This takes you directly to John's original writeup on this site click here
The first published account of the algorithm is in the proceedings of the ISAMA 11 Conference (Chicago, June 2011). To view or download a Word version click here About 3 Mbytes.
An overview of the algorithm. click here
The gasket is as interesting as the shapes themselves, and study of it helps to explain why the algorithm works. For a study of the gasket and its average width click here
An interesting account of the algorithm with some examples having quite nice graphics can be found on Paul Bourke's fractal web site. click here
An example can be more useful than a bunch of verbiage. To view C code for the circle case click C code. It is only about 200 lines long, including an output of a Postscript graphics file and a text output with a list of the data generated. You must be familiar with computer programming to work with this. You may cut-and-paste it into your own program if you wish. If you compile and run it you can generate your own images. The graphics output is a "generic Postscript" file and can be opened and rasterized with Photoshop or Photoshop Elements.
Current status of studies by John and others click here
A million circle example click here
Where does statistical geometry fit within the wider picture? click here
Does the statistical geometry algorithm work in 3 dimensions? click here
The "holes" in a circle pattern have interesting features click here
The statistical distribution of nearest-neighbor distances in a circle fractal have been studied. click here
The effect of shape on "packability" has been studied. click here
The statistics of trials and placements are studied in a report. click here
Non-uniform probability. click here
Grouped shapes -- a different form of the algorithm. click here
What shapes can be fractalized? click here
How can one find the nearest neighbors of a given shape? click here This study led to the discovery of a rather odd form of highly-constrained random graph.
Many of my fractal images have been made up as mug designs on Zazzle. You can see all of John's mug designs on the Zazzle site by clicking here. mugs
I have collected many images with explanatory text into a colorful 20-page "fractal art and math Coffee Table Book" under the title STATISTICAL GEOMETRY. To see and/or purchase it on the lulu web site click book If this does not work for any reason just search lulu with the string "john shier".
The image at the top of the page shows fractalized 7-tooth "gears". Log-periodic color.
The author is inclined to wonder if what is described here is not merely an "algorithm", but perhaps a "property of space itself".
I am happy to hear from people interested in this topic and can help if you want to get started on your own images. I am at johnart(atsign)frontiernet[dot]net.