2016/12/30 by Matin Amini, Majid Jahangiri, Amini, Matin +1
Computer Science · Mathematics · #11B25(Secondary) #11B99(Primary) #Cellular Automata and Applications #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1612.09481
openalex publication_date 2016/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A sequence is a fractal sequence if it contains itself as a proper subsequence. (The self-containment property resembles that of visual fractals) A doubly fractal sequence of integers is defined by operations called upper trimming and lower trimming. C. Kimberling proved that signature sequences are doubly fractal and conjectured the converse. This article gives a procedure for constructing doubly fractal sequences and proves Kimberling's conjecture.