Tuesday, July 19, 2011

Interactive Demonstrations - Computable Document Format

Wolfram Research supplies a free plug-in for viewing and interacting with online documents saved from Mathematica in Computable Document Format (CDF) - the plug-in can be downloaded from here. I thought that I would try it out on a few of my interactive Mathematica demonstrations, and here are the (draft) results for you to enjoy:
  1. Topographic String: This grows a 1-dimensional self-organising map, starting from 3 nodes and progressively inserting additional nodes. It is an implementation of the SOM training method that I published in 1988: "Self-organising multilayer topographic mappings", Proceedings of 2nd International Conference on Neural Networks (San Diego, USA), pp. I/93-I/100 - an online version is available here.
  2. Ising Model: This simulates a 2-dimensional Ising model, and it allows you to dynamically vary the clique factors for the 4 distinct types of 2-clique (i.e. N/S, E/W, NE/SW, SE/NW) to see how the Ising model behaves. It is an implementation of the Ising model simulations described in a report that I wrote in 1985: "The implications of Boltzmann-type machines for SAR data processing: a preliminary survey", RSRE technical report, 3815 - an online version is available here.
  3. BZ Reaction: This simulates the Belousov–Zhabotinsky reaction-diffusion system - it's very pretty.
  4. Current Algebra: This interactively computes commutators of products of current operators - it's a bit inflexible, but it shows some interesting Mathematica techniques in action.
  5. IMO 2011: This is hot off the press in response to Terence Tao's Minipolymath3 project: 2011 IMO, which plans to work on Q6 of the 2011 International Mathematics Olympiad. I have implemented an interactive version of Q6, so you can get an intuitive feel for the geometry involved. Update: I see that TT eventually decided to go with Q2 rather than Q6. Oh well, my interactive Q6 is fun to play with anyway.

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