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
- 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).
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.
For drawing the Dirichlet domain for a uniform lattice in SL(2,R). See the corresponding expository note here.
For drawing Apollonian gaskets.
For drawing Soddy sphere packings.
For tiling the plane by geodesics (Markoff spectrum, Zaremba).
For computing the Hausdorff dimension of certain Cantor sets
(the Jenkinson-Pollicott algorithm), giving a counterexample to Hensley's conjecture (a generalization of Zaremba).
For drawing low-lying horospheres in (infinite volume) hyperbolic space.
For drawing low-lying horocycles in the hyperbolic plane.
For drawing thin Pythagorean cones, labelled by primality of the hypotenuse, etc.
For drawing paths of the (3x+1)-Map.
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")!
program for making pictures of these fractals: