Randomness and Fractal Functions on the Sierpinski Triangle

Abstract

AbstractThe notion of fractal and its inherent characters are, in general, explained through the classical examples Cantor set and Sierpinski triangle. This article incorporates the probability and randomness on the dyadic Sierpinski triangle as follows. The construction process of dyadic Sierpinski triangle starts with an equilateral triangle as an initiator. Then, the generator divides the initiator into four equal triangles, by connecting the midpoints of three sides and removing the middle interior triangle with probability \((1-p)\), here the probability gears the randomness. Further, the homogeneous relation between the fractal dimension of the dyadic Sierpinski triangle and its randomness is investigated. Finally, the fractal interpolation function with variable scaling is implemented on the Sierpinski triangle by defining its Laplacian.