One-side peano curves of fractal genus 9

This paper completes the analysis (begun by E.V. Shchepin and the author in 2008) of regular Peano curves of genus 9 in search of a curve with the minimum square-to-linear ratio. One-side regular Peano curves of genus 9 are considered, and, among these curves, a class of minimal curves with a square-to-linear ratio of 5 2/3 is singled out. A new language to describe curves is introduced which significantly simplifies the coding of these curves.