2013/05/04 by Grenville J. Croll, Croll, Grenville J.
Computer Science · Mathematics · Neuroscience · #Algorithm #Arithmetic #Artificial intelligence #Binary number #Cognitive Science and Education Research #Combinatorics #Commentz-Walter algorithm #Computability, Logic, AI Algorithms #Computer science #Discrete mathematics #Entropy (arrow of time) #FOS: Computer and information sciences #Mathematical physics #Mathematics #Neural Networks and Applications #Other Computer Science (cs.OH) #Physics #Prime (order theory) #Prime number #Pseudorandom binary sequence #Quantum mechanics #String (physics) #String searching algorithm #cs.OH
paper · pdf · doi:10.48550/arxiv.1305.0954
16 Pages, 7 Tables, 6 Colour Figures. Presented at ANPA 34, Rowland's Castle, Hampshire, England, August 2013
openalex publication_date 2013/05/04 · arxiv created 2013/09/15 · arxiv updated 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string. We successfully test the algorithm in the fields of Prime Number Theory (where we prove explicitly that the sequence of prime numbers is not periodic), Human Vision, Cryptography, Random Number Generation and Quantitative Finance.