Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze a...

The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The q...

In this paper, we give the Hausdorff dimensions of certain sets of real numbers described in terms of the α-Lüroth expansion.

OBJECTIVES Fractal geometry is a tool used to characterize irregularly shaped and complex figures. It can be used not only to generate biological structures (e.g., the human renal artery tree), but also to derive parameters such as the fractal dimension in order to quantify the shapes of structures. As such, it allows user-independent evaluation and does not rely on the experience level of the ...

Two groups of aggregates with fractal dimensions of 1.81 ( 0.09 and 2.33 ( 0.07 were generated by coagulation of latex microspheres (2.84 μm) in a Jar-test (paddle-mixing) device. The collision rates between these fractal aggregates (200-1000 μm) and small (1.48 μm) particles were measured for individual aggregates that had settled through a suspension of the small particles. Aggregate permeabi...

We introduce fractal liquids by generalizing classical liquids of integer dimensions d = 1, 2, 3 to a fractal dimension df . The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid drop...

Box-covering algorithm is a widely used method to measure the fractal dimension of complex networks. Existing researches mainly deal with the fractal dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the fractal dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and gra...

We report a numerical study of van der Waals adsorption and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distribution of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to cros...

Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are studied within inertial and dissipative range scales in an attempt to relate changes in their se...