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Today, I have been playing a little bit with Apollonian circle packings. Here is the code I wrote in Mathematica to visualize such packings (see below for an example).

Attachment: 

apolloniancirclepackings.nb

Recently, I have been doing experiments involving q-binomial coefficients in Mathematica. Starting with version 7, Mathematica is prepared for some q-business; in particular, there exists a function named QBinomial giving the q-analog of Binomial. However, this implementation turned out to not be fast enough for my needs. Here is an alternative approach which is not only way faster but provides a full factorization. read more »