  The roughening of expanding flame fronts by the accretion of cusp-like
singularities is a fascinating example of the interplay between instability,
noise and nonlinear dynamics that is reminiscent of self-fractalization in
Laplacian growth patterns. The nonlinear integro-differential equation that
describes the dynamics of expanding flame fronts is amenable to analytic
investigations using pole decomposition. This powerful technique allows the
development of a satisfactory understanding of the qualitative and some
quantitative aspects of the complex geometry that develops in expanding flame
fronts.
