Study on properties of general Sierpinski fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. Like other fractals, general Sierpinski fractals are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. In [22], the authors the geometric modelling of a class of general Sierpinski fractals and their geometric ...

Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....

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 ...

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...

Self-affinity and self-similarity are fundamental concepts in fractal geometry. In this paper, they are related to collage grammars syntactic devices based on hyperedge replacement that generate sets of collages. Essentially, a collage is a picture consisting of geometric parts like line segments, circles, polygons, polyhedra, etc. The overlay of all collages in a collage language yields a frac...

The computation of the Hausdorff measure of fractals is the basic problem in fractal geometry. However, this is very difficult. The genetic algorithm is one of optimization algorithms to resolve complicated problems of wide scope, and has great capabilities in self-organizing, self-adaptation and self-learning. Lifeng Xi professor put forward to the thought of computing the Hausdorff measure of...

This paper introduces a new approach to represent logic functions in the form of Sierpinski Gaskets. The structure of the gasket allows to manipulate with the corresponding logic expression using recursive essence of fractals. Thus, the Sierpinski gasket’s pattern has myriad useful properties which can enhance practical features of other graphic representations like decision diagrams. We have c...

The multiband properties of self-similar fractals can be advantageously exploited to design multiband frequency selective surfaces (FSS). A Sierpinski dipole FSS has been analyzed and measured and the results show an interesting dual-band behavior. Furthermore a near-field measurement technique is applied to characterize the FSS response to different angles of incidence. Finally, it will be sho...

This paper describes the theories and techniques for designing linear and planar fractal arrays and compare their radiation pattern with conventional arrays. Fractals are recursively generated object having fractional dimension. We have compared radiation pattern of cantor linear arrays with conventional linear arrays using MATLAB program. Another program was developed to characterize the radia...