A lot of natural structures in industry applications can be hardly described by conventional methods – mostly statistic tools, because they are complex and irregular. A relatively new approach is the application of the fractal geometry that is successfully used in science, but an application in industry is sporadic and experimental only. However, the fractal geometry can be used as a useful too...

Fractals at T = T c due to instanton-like configurations Abstract We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter at the critical point (T = T c) we show that instanton-like configurations, corresponding to...

What is it that makes a face beautiful Average faces obtained by photographic or digital blending are judged attractive but not optimally attractive digital exagger ations of deviations from average face blends can lead to higher attractiveness ratings My novel approach to face design however does not involve blending at all Instead the image of a female face with high ratings is composed from ...

In his groundbreaking work, ‘The Fractal Geometry of Nature’ (Mandelbrot, 1982), Benoit Mandelbrot described how fractals could account for a long list of natural forms ranging from trees to coastlines. Two recent studies in Science and The EMBO Journal have suggested that chromatin and the nucleoplasmic space surrounding it should be added to the fractal list. Fractals are ‘self-similar’, mean...

From graphic design to stock market predictions, applications offtactal geometry permeate fields in every way. The depiction offtactals also has substantial artistic intrigue. Mathematical graphs displaying multiple dimensions of self-similarity reveal highly evocative perceptions of depth and design. Such a fascination in sight can also be perceived in sound. This n:searclt explains the depict...

In this survey we give a report on some recent results obtained in the studies of hyperbolic manifolds by means of fractal geometry. Emphasis has been put on results derived in the quantitative and qualitative fractal analysis of long term geodesic dynamics on hyperbolic manifolds.

The extension of the concepts of the Fractal Geometry [Mandelbrot 1983] toward the life sciences has brought a significant progress in understanding complex functional properties and morphological features that characterise cells and tissues. It has even be argued that fractal geometry might provide a coherent description of the design principle underlying living organisms. Fractals fulfil a ce...

Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the “eternal...

In this paper , a relationship between the classical theory of computat ion and fract al geometry is est ablish ed. It erated Function Syst ems are used as tool s to define fractals. It is shown t hat two questions about Iterat ed Function Systems are und ecidable: to t est if t he attractor of a given It erat ed Fun ction Syst em and a given line segment int ersect and to test if a given It er...

The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The permeation of oxygen and carbon dioxide through the fractal membrane is measured and validated th...