  Laplacian growth, associated to the diffusion-limited aggregation (DLA) model
or the more general dielectric-breakdown model (DBM), is a fundamental
out-of-equilibrium process that generates structures with characteristic
fractal/non-fractal morphologies. However, despite of diverse numerical and
theoretical attempts, a data-consistent description of the fractal dimensions
of the mass-distributions of these structures has been missing. Here, an
analytical description to the fractal dimensions of the DBM and DLA is provided
by means of a recently introduced general dimensionality equation for the
scaling of clusters undergoing a continuous morphological transition.
Particularly, this equation relies on an effective information-function
dependent on the Euclidean dimension of the embedding-space and the control
parameter of the system. Numerical and theoretical approaches are used in order
to determine this information-function for both DLA and DBM. In the latter, a
connection to the R\'enyi entropies and generalized dimensions of the cluster
is made, showing that DLA could be considered as the point of maximum
information-entropy production along the DBM transition. These findings are in
good agreement with previous theoretical and numerical results (two- and
three-dimensional DBM, and high-dimensional DLA). Notably, the DBM dimensions
can be conformed to a universal description independently of the initial
cluster-configuration and the embedding-space.
