Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory

Qianli Zhou and Yong Deng

Chaos, Solitons & Fractals, 2023, vol. 166, issue C

Abstract: Graphics with fractal features are usually generated using the Iterated Function System (IFS). IFS can generate the entire family of Sierpinski gaskets by performing different operations on the attractors. As the most classical graphic, Sierpinski gasket can also be generated using mod(n,2). Dempster–Shafer Theory (DST), as a mathematical theory about evidence, models information on the all possible combination states (power set), which relates to 2n. In this paper, we explore the relationship between the Sierpinski gasket and matrix calculus in DST, which is the first time to connect fractal theory and DST from the perspective of geometry. In addition, based on the generation process of the matrices, we propose a method to generate the Sierpinski Gasket using the Kronecker product.

Keywords: Fractal; Sierpinski gasket; Dempster–Shafer theory; Belief functions; Belief matrix (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011419

DOI: 10.1016/j.chaos.2022.112962

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