  Unbiased shuffling algorithms, such as the Fisher-Yates shuffle, are often
used for shuffle play in media players. These algorithms treat all items being
shuffled equally regardless of how similar the items are to each other. While
this may be desirable for many applications, this is problematic for shuffle
play due to the clustering illusion, which is the tendency for humans to
erroneously consider 'streaks' or 'clusters' that may arise from samplings of
random distributions to be non-random. This thesis attempts to address this
issue with a family of biased shuffling algorithms called cluster diffusing
(CD) shuffles which are based on disordered hyperuniform systems such as the
distribution of cone cells in chicken eyes, the energy levels of heavy atomic
nuclei, the eigenvalue distributions of various types of random matrices, and
many others which appear in a variety of biological, chemical, physical, and
mathematical settings. These systems suppress density fluctuations at large
length scales without appearing ordered like lattices, making them ideal for
shuffle play. The CD shuffles range from a random matrix based shuffle which
takes $O(n^3)$ time and $O(n^2)$ space to more efficient approximations which
take $O(n)$ time and $O(n)$ space.
