Tom Stoppard's play Arcadia (Faber and Faber, 1993) places fractals and
chaos in the discoveries of a 19th century mathematical
prodigy, Thomasina Coverly, and in fluctuations of the grouse population of
the presentday Coverly estate. 
The play moves back and forth between the
two times, until the end of the play, Scene Seven, when the times interpenetrate. 
Thomasina's rebellions against determinism and Euclidean geometry provide an
excellent introduction to the motivations of fractal geometry and chaotic dynamics. 

Fractals may appear in a more subtle fashion in the structure of the play.
Here is an example, first observed by Joise Rodberg. 
Be sure to consult Bob Devaney's Arcadia website
http://math.bu.edu/DYSYS/arcadia. 