Related papers: Sierpinski Gaskets for Logic Functions Representat…
The {\it Sierpi\'nski fractal} or {\it Sierpi\'nski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the…
This paper studies presentations of the Sierpinski gasket as a final coalgebra for functors on several categories of metric spaces with additional designated points. The three categories which we study differ on their morphisms: one uses…
This paper presents the graphic representation in the z-plane of the first three iterations of the algorithm that generates the Sierpinski Gasket. It analyzes the influence of the f(z) map when we represent fractal images.
One of the ways that analysis on fractals is more complicated than analysis on manifolds is that the asymptotic behavior of the spectral counting function $N(t)$ has a power law modulated by a nonconstant multiplicatively periodic function.…
The study of Julia sets gives a new and natural way to look at fractals. When mathematicians investigated the special class of Misiurewicz's rational maps, they found out that there is a Julia set which is homeomorphic to a well known…
We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification.
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
By slight modification of the data of the Sierpinski gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated…
In this paper, we have obtained bounds for the box dimension of graph of harmonic function on the Sierpi\'nski gasket. Also we get upper and lower bounds for the box dimension of graph of functions that belongs to $\text{dom}(\mathcal{E}),$…
In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\'nski Gasket (SG). We also provide some results related to constrained approximation…
We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket to formulate and prove analogues of the strong Szego limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of…
We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length $mn$ for all $n$, and certain $\12-$order Sobolev norms on the graph paper lines. We also…
The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket ({\bf $SG$}) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of polynomials and power series on…
We obtain formulas for the spectral zeta function of the Laplacian on symmetric finitely ramified fractals, such as the Sierpinski gasket, and a fractal Laplacian on the interval. These formulas contain a new type of zeta function…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski…
Fractal lattices are self-similar structures with repeated patterns on different scales. As in other aperiodic lattices, the absence of translational symmetry can give rise to quantum localization effects. In contrast to low-dimensional…