Title:
 The 2 dimensional quantum random walk and appearance of fractal structures.

 Abstract:
  Fractal-like structures may be formed by the aggregation of particles
 moving randomly, in a phenomenon called "diffusion limited
 aggregation". We investigate how quantum effects may modify the
 formation of such fractal structures. Quantum random motion in 2-dimensional
 space is modeled numerically using a Hadamard transformation.  We find that
 quantum coherence greatly speeds up the formation of fractals.  Quantum
 interference effects on the shape of the fractal are discussed.