Diffusion on nonexactly decimable tree-like fractals

Hilbert R-tree: An Improved R-tree using Fractals

We propose a new R-tree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting approach in R-trees. This is done by proposing an ordering on the R-tree nodes. This ordering has to be 'good', in the sense that it should group 'similar' data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (M...

Random Fractals and Tree - Indexed Markov

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the Moran-like deterministic or random recursive constructions considered by various authors. Among other applications, we consider various extensions of Mandelbrot's...

Finite Size Scaling Analysis of Biased Diffusion on Fractals

Diffusion on a T fractal lattice under the influence of topological biasing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormalization group approach on infinite system as a consequence of logarithmic diffusion. Within the scheme, logarithmic diffusion is proved on the basis of an analysis of various temporal sca...

Dynamic Scaling of an Adsorption-Diffusion Process on Fractals

We study numerically a dynamic scaling of a diffusion process involving the Langmuir type adsorption. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations. We study further the dynamic scaling law on fractal surfaces. The adsorption-diffusion process obeys the fracton dynamics on the fractal surfaces.

Tree-based generation of languages of fractals