On the fibbinary numbers and the Wythoffarray

2024/05/28 by A. J. Macfarlane, Macfarlane, A. J.
Computer Science · #11A67 #11B83 #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.18128

openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper defines the set fib of fibbinary numbers and displays its structure in the form of a table of a specialised type, and in array form. It uses the Zeckendorf representation n ∈ N to define a bijection Z between N and fib. It is proved that the fibbinary array is the image under Z of the famous Wythoff array. The fibbinary table proves useful pictorial insight into the fractal defined by the Wythoff array. The Wythoff table, obtained as the image under the inverse of Z of the fibbinary table, leads to a simpler view of the fractal, and may be compared with the (1938) Steinhaus tree.

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