Study on properties of Sierpinski-type fractals, including dimension, measure, connectedness, Lipschitz equivalence, etc are very interesting. Although there have been some very nice results were obtained, there is still a long way to go to solve all the problems. In order to facilitate understanding of these results and further study, in this paper, we simulate this kind of fractals and their ...

Antipolynomial of a complex polynomial is generated by applying iteration on a function z +c for d>=2. This complex function has been intense area for researcher. If we use transcendental function like sine, cosine etc with antipolynomial, i.e. cos ( z +c), it becomes a more elite area to design beautiful images of fractal. The purpose of this paper is to generate the fractals using function co...

The attractors of Iterated Function Systems in Euclidean space IFS fractals have been the subject of great interest for their ability to visually model a wide range of natural phenomena. Indeed computer-generated plants are often modeled using 3D IFS fractals, and thus their extent in virtual space is a fundamental question, whether for collision detection or ray tracing. A great variety of alg...

Owing to the prevalence of fractal patterns in natural scenery and their growing impact on cultures around the world, fractals constitute a common feature of our daily visual experiences, raising an important question: what responses do fractals induce in the observer? We monitored subjects' EEG while they were viewing fractals with different fractal dimensions, and the results show that signif...

In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are most often not groups. We show that nonetheless those fractals that come from iteration of affine mappings in R have a spectral duality which is instead based...

This article aims at providing a new theoretical insight into the fundamental question of the origin of truncated fractals in biological systems. It is well known that fractal geometry is one of the characteristics of living organisms. However, contrary to mathematical fractals which are self-similar at all scales, the biological fractals are truncated, i.e. their self-similarity extends at mos...

Impossible objects are a type of optical illusion involving ambiguous visual descriptions of figures that cannot physically exist. It is shown by way of example that such objects can be further developed using standard fractal techniques to create new, more complex designs that retain the perceptual illusion, sometimes allowing additional illusions to emerge from the process. The balanced Pytha...

Hausdorff dimensions of level sets generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those the topological dimension was defined. this paper we start to study 1-Hölder-? fractals. This is related some sort “thickness”, “conductivity” properties The main concept our D?(?,F) which essential supremum a function fractal F. We ...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible \backward" extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these tec...