The Fibonacci Space-Filling Curve
Abstract
Can you stretch and reform a curve such that it fills a square completely? This question dates back to the late 19th century—the origin of space-filling curves. It was proven affirmatively by many great mathematicians. In this document, we reconsider the problem and present a different proof using the Cartesian product of Fibonacci substitution with itself. Our construction differs from other curves by the particular ordering produced by the Cartesian product of Fibonacci substitutions and the iterative geometric design induced by it.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Digital Image Processing Techniques
Publication details
- Journal / source
- Geometry
- Volume
- 3
- Issue
- 3
- Pages
- 14–14
- Publication date
- 20 July 2026
- Language
- EN