It is widely accepted that the complexity and biodiversity of life on earth that we observe today began as a density fluctuation in a giant molecular cloud roughly sixteen galactic years ago. After about sixteen more galactic rotations, our biosphere will return to the interstellar medium. This talk will first investigate models whereby simple systems may evolve into a complex state. The emergence of complex molecules such as amino acids may be described by prebiotic chemical evolution as demonstrated by the Miller experiment. Mathematical models of biological evolution can exhibit complex rearrangements – or extinction events – spanning several decades in size and time durations. The predicted powerlaw in the number of species affected by a given extinction event is also evidenced by the fossil record. Similar spatial-temporal powerlaw behavior is observed in the cellular automaton – The Game of Life. The emergence of fractal structures in biology and chaos in population dynamics is then discussed. Finally, the larger question of the possible distribution of life in the universe is addressed. It is assumed that if life is plentiful, then its distribution should be the same as that of the baryonic matter in the universe. A dramatic example of self-similarity in the possible distribution of life in the universe over immense size scales is illustrated comparing the distribution of mitochondria in a yeast cell to the galaxy distribution over 2 billion light years as recorded by the 2dF Galaxy Redshift Survey.