  Conformal mapping models are used to study competition of noise and
anisotropy in Laplacian growth. For that, a new family of models is introduced
with the noise level and directional anisotropy controlled independently.
Fractalization is observed in both anisotropic growth and the growth with
varying noise. Fractal dimension is determined from cluster size scaling with
its area. For isotropic growth we find d = 1.7, both at high and low noise. For
anisotropic growth with reduced noise the dimension can be as low as d = 1.5
and apparently is not universal. Also, we study fluctuations of particle areas
and observe, in agreement with previous studies, that exceptionally large
particles may appear during the growth, leading to pathologically irregular
clusters. This difficulty is circumvented by using an acceptance window for
particle areas.

Statistical Mechanics;Soft Condensed Matter;Chaotic Dynamics