In this paper the theory of Carry Value Transformation (CVT) is designed and developed on a pair of n-bit strings and is used to produce many interesting patterns. One of them is found to be a self-similar fractal whose dimension is same as the dimension of the Sierpinski triangle. Different construction procedures like L-system, Cellular Automata rule, Tilling for this fractal are obtained whi...

On the Sierpinski Gasket (SG) and related fractals, we define a notion of conformal energy Eφ and conformal Laplacian ∆φ for a given conformal factor φ, based on the corresponding notions in Riemannian geometry in dimension n 6= 2. We derive a differential equation that describes the dependence of the effective resistances of Eφ on φ. We show that the spectrum of∆φ (Dirichlet or Neumann) has si...

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the Cantor set and Sierpinski carpet as special cases. Also randomized versions of these fractals are treated. The general result is that the diffraction intensiti...

Abstract. The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of polynomials and power series on SG has been developed by one of us and his coauthors. We build on this body of work to construct certain analogs of classical orthogonal polynomials (OP) on S...

In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. particular, consider the strong form equation using standard graph Laplacian matrices and also weak forms derived length or área measure a discrete approximation fractal set. We then introduce procedure normalize obtained diffusions, that is, way renormalization constant need...

Recent progress in the controllable functionalization of graphene surfaces enables experimental realization complex functionalized nanostructures, such as Sierpinski carpet (SC) fractals. Herein, we model SC fractals formed by hydrogen and fluorine patterns on surfaces, namely, H-SC F-SC, respectively. We then reveal their electronic properties quantum transport features. From calculated result...

We study the problem of adsorption of self-interacting linear polymers situated in fractal containers that belong to the three-dimensional (3d) Sierpinski gasket (SG) family of fractals. Each member of the 3d SG fractal family has a fractal impenetrable 2d adsorbing surface (which is, in fact, 2d SG fractal) and can be labelled by an integer b (2 ≤ b ≤ ∞). By applying the exact and Monte Carlo ...

The dynamical systems on the classical fractals can naturally be obtained with help of their iterated function systems. In recent years, different ways have been developed to define self similar sets. this paper, we give composition functions by using expanding and folding mappings which generate Sierpinski Gasket via escape time algorithm. These also indicate fractal. We express code represent...

Abstract This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in mathematical reasoning displayed university Masters level lesson on fractals. During whole class small group discussions, eleven students, guided by an instructor, engage inductive about area perimeter of Sierpinski triangle, unique object with zero infinite pe...