Prof. Sussman's Reading List
KAM: Automatic Planning and Interpretation of Numerical 
Experiments Using Geometrical Methods<p><pre><code>  * By Kenneth Man-Kam Yip, 1989
  * Coolest PhD thesis ever!
  * Solve problems using graphs.
  * So cool!
</code></pre>
This caught my interest: <a href="http://dspace.mit.edu/handle/1721.1/7025" rel="nofollow">http://dspace.mit.edu/handle/1721.1/7025</a><p>It is indeed one of the coolest papers and programs ever. KAM is a smart ODE solver, written in ZetaLisp on a Symbolics. It analyzes 2D pointsets created by any 2d equations, esp. non-linear ones. Typically a system of ordinary or partial differential equations, with a set of boundary and initial conditions. A typical non-linear physical system.
It creates MST's (Minimal spanning trees) of the calculated points to get the shape and number of curves, to see the number of clusters (checking the distance of the curves), and if the curves are linear or space filling.
Then the phase space is searched for initial states and end conditions, and to get useful summaries. It cannot do shape matching though, so repetitions and mirroring are not detected as such.<p>The goal is to get high-level descriptions of the model and the numerical dataset, and at which parameter ranges and conditions the system falls into chaos. Chaotic systems are bad for predictability but mostly good for engineering purposes.