PROGRAMS:
Here are some Mathematica programs to make the pictures and movies on this site. This is just for fun. Note: I'm a mathematician, not a computer programmer; these are done poorly, inefficiently, and poorly. They get the job done (sometimes). Right-click to download.Feel free to play around and make your own pictures, and if you end up using them, please acknowledge the source. All files (c) 2018.
- Added 3/2018:
Values of Omega(F_n), Omega(L_n), and Omega(M_n) for Fibonacci F_n, Lucas L_n, and Mersenne M_n sequences.
- Added 12/2017:
For constructing crystallographic sphere packings. See accompanying
letter.
- Added 11/04/2013:
For finding low-lying closed geodesics over a given real quadratic field .
- Added 10/24/2013:
For drawing Apollonian-3 gaskets, dual configurations, and orbits (for Xin Zhang).
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Added 11/30/2011: For playing around with the Explicit Formula for the Riemann zeta function. See the corresponding file for MAT 310 (Complex Analysis) here.
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For drawing the Dirichlet domain for a uniform lattice in SL(2,R). See the corresponding expository note here.
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For drawing Apollonian gaskets.
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For drawing Soddy sphere packings.
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For tiling the plane by geodesics (Markoff spectrum, Zaremba).
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For computing the Hausdorff dimension of certain Cantor sets
(the Jenkinson-Pollicott algorithm), giving a counterexample to Hensley's conjecture (a generalization of Zaremba).
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For drawing low-lying horospheres in (infinite volume) hyperbolic space.
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For drawing low-lying horocycles in the hyperbolic plane.
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For drawing thin Pythagorean cones, labelled by primality of the hypotenuse, etc.
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For drawing paths of the (3x+1)-Map.
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A long long time ago (1998?), Sam Payne and I played around with Conway's audioactive decay sequence (mod 2).
We found that there were exactly two limiting fractal structures (other than concatenations of "boring old 1110")!
Here's a
program for making pictures of these fractals:
