Content deleted Content added
Citation bot (talk | contribs) Removed parameters. | Use this bot. Report bugs. | #UCB_CommandLine |
m →Self-similarity: Changed the language in the last very short paragraph of Self-Similarity section. The symmetry relations cannot be both exactly the same and slightly altered. The new language reflects this fact. |
||
Line 108:
The dyadic monoid itself has several interesting properties. It can be viewed as a finite number of left-right moves down an infinite [[binary tree]]; the infinitely distant "leaves" on the tree correspond to the points on the Cantor set, and so, the monoid also represents the self-symmetries of the Cantor set. In fact, a large class of commonly occurring fractals are described by the dyadic monoid; additional examples can be found in the article on [[de Rham curve]]s. Other fractals possessing self-similarity are described with other kinds of monoids. The dyadic monoid is itself a sub-monoid of the [[modular group]] <math>SL(2,\mathbb{Z}).</math>
Note that the Cantor function bears more than a passing resemblance to [[Minkowski's question-mark function]]. In particular, it obeys
== Generalizations ==
| |||