Minimal Self-Similar Peano Curve of Genus 5 × 5¹

Yu. V. Malykhin^a^,* and Corresponding Member of the RAS E. V. Shchepin^a^,**

^aSteklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991 Russia

Correspondence to: *e-mail: malykhin@mi-ras.ru
Correspondence to: **e-mail: scepin@mi-ras.ru

¹The article was translated by the authors.

Received 22 January, 2020

Abstract—The paper presents a plane regular fractal Peano curve with a Euclidean square-to-line ratio (L₂-locality) of $5\frac{{43}}{{73}}$, which is minimal among all known curves of this class. The presented curve has a fractal genus of 25. Performed calculations allow us to state that all the other regular curves with a fractal genus not exceeding 36 have a strictly greater square-to-line ratio.

Keywords: space-filling curves, Peano curves, square-to-line ratio, regular fractal curves

DOI: 10.1134/S1064562420020155

Minimal Self-Similar Peano Curve of Genus 5 × 51

Minimal Self-Similar Peano Curve of Genus 5 × 5¹