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 $5\frac 23$ is singled out. A new language to describe curves is introduced which significantly simplifies the coding of these curves.