Voronoi Expert Found!

Alan Shaw noticed my blog post Help! Voronoi expert wanted and kindly volunteered to share his 20+ years of Voronoi-specific experience.

From my blog post's description of the problem (plus a few other details), he was able to develop a Flash applet to show the Voronoi relationships among regular lattice cells as the lattice is systematically deformed. This applet is a great example of data visualization.

By playing with this applet, Bill Sethares and Andy Milne (my partners in musical heresy) were able to deduce the relevant mathematical relationships. They're now working out the details & proofs with Alan.

Data visualization is remarkably powerful, isn't it? As the Overview to Wikipedia's article on data visualization states (or, at least, as it stated when I wrote this):

"The main goal of data visualization is to communicate information clearly and effectively through graphical means...To convey ideas effectively, both aesthetic form and functionality need to go hand in hand, providing insights into a rather sparse and complex data set by communicating its key-aspects in a more intuitive way. "

Fundamentally, JIMS is nothing more than a tool for data visualization (and control), whose aim is to expose, to its users' intuition, the invariant relationships in music just as Alan's applet exposed the invariant properties of a systematically-deformed lattice.

Thanks, Alan! :-)