▪ Abstract The retinal circulation of the normal human retinal vasculature is statistically self-
similar and fractal. Studies from several groups present strong evidence that the fractal …

We re-evaluate the experimental data concerning the large scale structure of the universe
utilizing the theoretical methods of modern statistical mechanics. This allows us to test the …

The dynamics of complex systems in nature often occurs in terms of punctuations, or
avalanches, rather than following a smooth, gradual path. A comprehensive theory of …

We introduce a new theoretical approach that clarifies the origin of fractal structures in
irreversible growth models based on the Laplace equation and that provides a systematic …

The fractal dimension (FD) can be used as a measure for morphological complexity in
biological systems. The aim of this study was to test the usefulness of this quantitative …

Irreversible fractal-growth models like diffusion-limited aggregation (DLA) and the dielectric
breakdown model (DBM) have confronted us with theoretical problems of a new type for …

THE process of diffusion-limited aggregation (DLA) is a common means by which clusters
grow from their constituent particles, as exemplified by the formation of soot and the …

We introduce and investigate a family of exactly self-similar nonrandom fractal measures,
each having stretched exponentially decreasing minimum probabilities. This implies that τ …

Abstract q-derivatives can be identified with the generators of fractal and multifractal sets
with discrete dilatation symmetries. Besides providing a natural language in which to …

We present a theory of branched growth processes, notably diffusion-limited aggregation
(DLA). Using a simple model of the dynamics of screening of competing branches, we …