On the box-counting dimension of graphs of harmonic functions on the Sierpiński gasket

By Abhilash Sahu, Amitabh Priyadarshi. 2020

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Abstract The objective of this paper is to study the box-counting dimension of graphs of fractal interpolation functions and harmonic functions on the Sierpinski gasket. Firstly, we give construction of a fractal interpolation function on the Sierpinski gasket and then with the help of fractal interpolation functions we show the existence of fractal functions in the space dom ( E ) consisting of all finite energy functionals on the Sierpinski gasket. Later, we provide bounds for the box-counting dimension of graphs of some functions belonging to the family of continuous functions which arise as fractal interpolation functions. Moreover, we also obtain bounds for the box-counting dimension of graphs of harmonic functions and piecewise harmonic functions. Also, we obtain upper and lower bounds for the box-counting dimension of graphs of functions that belong to dom ( E ) .

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4d529f8969fe99a13821fb9749e28650da0791ef