The Fibonacci Space-Filling Curve
Geometric Topology
2024-06-11 v1
Abstract
Can you stretch and reform a curve such that it fills a square completely? This question dates back to 18th century, the origin of space-filling curves. It was proved affirmatively by many great mathematicians. In this document, we reconsider the problem and present a different proof using Cartesian product of Fibonacci substitution with itself. Our construction differs from other curves by design.
Cite
@article{arxiv.2406.05583,
title = {The Fibonacci Space-Filling Curve},
author = {Mustafa Ismail Ozkaraca},
journal= {arXiv preprint arXiv:2406.05583},
year = {2024}
}