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.
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