Cantor function: Difference between revisions

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==Self-similarity==

The Cantor function posses several [[symmetry|symmetries]]. OneFor <math>0\le x\le 1</math>, there is a reflection symmetry:

:<math>c(x)=1-c(1-x).</math>

The other isand a pair of magnifications, one on the left and one on the right:

:<math>c\left(\frac{x/}{3}\right) = \frac{c(x)/}{2}</math>

and

:<math>c\left((\frac{x+2)/}{3}\right) = \frac{1+c(x)/2 + 1/}{2}</math>

== Generalizations ==