We study the self-similar structure of electromagnetic showers and introduce
the notion of the fractal dimension of a shower. Studies underway of showers in
various materials and at various energies are presented, and the range over
which the fractal scaling behaviour is observed is discussed. Applications to
fast shower simulations and identification, particularly in the context of
extensive air showers, are also discussed.Comment: Talk to be presented at the XI International Symposium on Very High
Energy Cosmic Ray Interaction