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In this note, we investigate the regularity of Cantor's one-to-one mappingbetween the irrational numbers of the unit interval and the irrational numbersof the unit square. In particular, we explore the fractal nature of this map byshowing that its H\"older regularity lies between 0.35 and 0.72 almosteverywhere (with respect to the Lebesgue measure).

About the multifractal nature of Cantor's bijection