Version 1
: Received: 17 February 2024 / Approved: 18 February 2024 / Online: 19 February 2024 (14:31:34 CET)
How to cite:
A Mageed, D.I. Fractal Dimension of Ismail’s Third Entropy with Fractal Applications to CubeSat Technologies and Education. Preprints2024, 2024020954. https://doi.org/10.20944/preprints202402.0954.v1
A Mageed, D.I. Fractal Dimension of Ismail’s Third Entropy with Fractal Applications to CubeSat Technologies and Education. Preprints 2024, 2024020954. https://doi.org/10.20944/preprints202402.0954.v1
A Mageed, D.I. Fractal Dimension of Ismail’s Third Entropy with Fractal Applications to CubeSat Technologies and Education. Preprints2024, 2024020954. https://doi.org/10.20944/preprints202402.0954.v1
APA Style
A Mageed, D.I. (2024). Fractal Dimension of Ismail’s Third Entropy with Fractal Applications to CubeSat Technologies and Education. Preprints. https://doi.org/10.20944/preprints202402.0954.v1
Chicago/Turabian Style
A Mageed, D.I. 2024 "Fractal Dimension of Ismail’s Third Entropy with Fractal Applications to CubeSat Technologies and Education" Preprints. https://doi.org/10.20944/preprints202402.0954.v1
Abstract
Entropy as a mathematical concept is the first of its own kind, and second to none.Barely one or two papers in literature have investigated fractal dimensions of very basic entropies, such as Shannon, Tsallis, and Rényi entropic expressions. This was a thoughtful inspiration to delve into a step forward towards a unified information- theoretic fractal theory. The storytelling of this current paper starts by introducing my third entropy formula, namely Ismail’s entropy, , as a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. Clearly, this would generate a fourfold unification with statistical mechanics as well as contemporary physics. Hence, this adds more credibility and weight for this study. The fractal dimension of , is identified in this paper. As an essential part of this work, it was influential to spotlight the importance of fractal geometry to space industry as well as education, which is crucial to develop our societies. Thus, some potential fractal applications to CubeSat Technologies and Education are highlighted. So, will the deep search for more ground-breaking research has come to an end. Certainly, not. This was another inspiration to propose new open problems to widen research gates to the scientific community for more research pathways. Consequently, the paper ends with closing remarks combined with some challenging open problems and the next phase of research.
Keywords
Fractal dimension; Ismail’s third entropy; CubeSat Technologies; Education
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
