PWIT Visualisation

Many questions involving random points in two or three dimensions are too difficult to answer via explicit formulas. Monte Carlo simulations provide numerical answers to individual problems but don't offer much theoretical insight. There is an alternative model, the PWIT, loosely interpretable as ``random points in infinite-dimensional space", which sacrifices realism to gain mathematical tractability. One can then compare theoretical predictions for the PWIT with Monte Carlo results in low dimensions.

In the picture below, the random points are the small discs. Each point has ``neighbor" points at random distances, the neighbor relationship indicated by lines. The neighbor points have their own neighbors, and so on. Mathematically the PWIT is an infinite structure; the picture shows the part of the PWIT within a certain distance of a reference ``root" point, positioned in the center of the window. More about the mathematics of the PWIT.

This site shows visualizations of one aspect of the math theory of the PWIT:

Starting with combinatorial optimization we consider the traveling salesman problem (TSP), minimum matching (MM), and minimum spanning tree (MST). Read how to run the simulation or just check MM on the menu and then start clicking on nodes.

After a while you may want to read why the picture sometimes looks wrong (but really isn't).

Version 0.96

Applet should produce picture within 45 seconds. Done when you see "Applet PWIT/PWITDemo.class started" in your browser bar.

More recent versions may be viewable at David Brightly (developer) page, which also explains why this may not work on Internet Explorer.

This material is based on work supported by the National Science Foundation under Grant DMS-0403062. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.