In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of the Gauss’s law, we consider the simple examples of the fields of homogeneous fractal distribution. The examples of gra...

In the present paper, the bounds on fractal dimension of Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) in R on a equispaced mesh are found. These bounds determine the conditions on the free parameters for fractal dimension of the constructed CHFIS to become close to 3. The results derived here are tested on a tsunami wave surface by computing the lower and upper bounds of th...

In this dissertation, the problem of the construction of Fractal Interpolation Surfaces and their application in image compression is studied. We give exact conditions, so that this construction is valid and we introduce some free parameters that make our model as flexible as possible. In addition, we compute the box-counting dimension of a Fractal Interpolation Surface. Finally, we give a new ...

Purpose – Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to gene...

The power-law dependence of the angle in the angular projection of galaxy distribution is explained by assuming that in the spherical shells within a small angle the distributions are also fractal, this local angular fractal gives the so-called local isotropy a precise meaning and thus realizes the Cosmological Principle in a fractal model in a rather strict way. If it possesses local angular f...

The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating complexity of non-fractal images. The modified Hausdorff fractal dimension stands on two features that weaken the requirement of presence of a shape and als...

Fractals are popular because of their ability to create complex images using only several simple codes. This is possible by capturing image redundancy and presenting the image in compressed form using the self similarity feature. For many years fractals were used for image compression. In the last few years they have also been used for face recognition. In this research we present new fractal m...