Fractal Dimension(D f ) Theory of Ismail’s Second Entropy(H q I ) with Potential Fractal Applications to ChatGPT, Distributed Ledger Technologies(DLTs) and Image Processing(IP)

Abstract

This work introduces my second entropy measure, Ismail’s second entropy, namely $(H_{1}^{q})$ is a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. The fractal dimension of $H_{1}^{q}$ is identified in this paper. Following this, some potential fractal applications to ChatGPT, Distributed Ledger Technologies(DLTs), and Image Processing are highlighted. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.