Fractal Brownian motions have been introduced as a statistical descriptor of natural images. We analyze the Gaussian scale-space scaling of derivatives of fractal images. On the basis of this analysis we propose a method for estimation of the fractal dimension of images and scale-space normalization used in conjunction with automatic scale selection assuming either constant energy over scale or...

Fractal Brownian motions have been introduced as a statistical description of natural images. We analyze the Gaussian scale-space scaling of derivatives of fractal images. On the basis of this analysis we propose a method for estimation of the fractal dimension of images and scale-space normalisation used in conjunction with automatic scale selection assuming either constant energy over scale o...

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. T...

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth anal...

From a “strange” case-Koch curve in Euclidean space, we introduce the concept of fractal geometry, and meanwhile, give the MATLAB programs and their operational results. Since a variety of phenomena in nature have fractal characteristics, yet it is difficult to simulate the natural features with fractal characteristics in Euclidean space. Therefore, in order to solve this problem, we apply frac...

This paper is in the form of an essay. It defines fractal tops and code space structures associated with set-attractors of hyperbolic iterated function systems (IFSs). The fractal top of an IFS is associated with a certain shift invariant subspace of code space, whence the entropy of the IFS, and of its set-attractor, may be defined. Given any ordered pair of hyperbolic IFSs, each with the same...

This work studies the problem of GPU thread mapping for a Sierpiński gasket fractal embedded in a discrete Euclidean space of n × n. A block-space map λ : Z2E 7→ Z 2 F is proposed, from Euclidean parallel space E to embedded fractal space F, that maps in O(log 2 log 2 (n)) time and uses no more than O(n) threads with H ≈ 1.58... being the Hausdorff dimension, making it parallel space efficient....

Let a be a positive real number, a < 1/2. A standard construction of a self-similar Cantor set in the plane starts with the unit square [0, 1]× [0, 1], replaces it with the four corner squares with sidelength a, then replaces each of those squares with their four corner squares of sidelength a, and so on. At the nth stage one has 4 squares with sidelength a, and the resulting Cantor set has Hau...

This contribution deals with the hypothesis of the existence of fractal structures in language which was proposed by Lud ek H reb cek in 1992. I will propose a systems-theoretical point of view in order to deene both an imbedding space appropriate to represent linguistic fractal structures and mappings between the observed data and the imbedding space.

This paper is an at tempt to model well decline in a vapor dominated reservoir with fractal geometry. The fractal network of fractures is treated as a continuum with characteristic anomalous diffusion of pressure. A numerical solver is used t o obtain the solution of the partial differential equation including adsorption in the fractal storage space. The decline of the reservoir is found t o ob...