Combinatorics and Space-Filling Curves

Robert Dickau has done many nice combinatorial diagrams with Mathematica. For example, here's some i like:

His home page has many more. You can also get many of his interactive Mathematica files at

You might also enjoy a combinatoric diagram i did. See: Number Of Ways To Loop n Points. (it was done with Mathematica v3. I'll update the notebook to v7 soon.)

loop thru n points

Possible loops with 5 points:

Many of Robert's work are about space filling curves. It is one of the math i learned in early 1990s that had a big effect on me. In short, it shows that there are same number of points of one side of a square to the square itself. At the time, it was a shock to mathematicians. See: Space-filling curve, and Xah's Top 10 Math Wonders.

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