- Title
- A sequential view of self-similar measures; or, what the ghosts of Mahler and Cantor can teach us about dimension
- Creator
- Coons, Michael; Evans, James
- Relation
- Journal of Integer Sequences Vol. 24, Issue 2, no. 21.2.5
- Relation
- https://cs.uwaterloo.ca/journals/JIS/VOL24/Coons/coons8.html
- Publisher
- University of Waterloo
- Resource Type
- journal article
- Date
- 2021
- Description
- We show that a missing q-ary digit set F ⊆ [0, 1] has a corresponding naturally associated countable binary q-automatic sequence f. Using this correspondence, we show that the Hausdorff dimension of F is equal to the base-q logarithm of the Mahler eigenvalue of f. In addition, we demonstrate that the standard mass distribution νF supported on F is equal to the ghost measure µf of f.
- Subject
- automatic sequence; Hausdorff dimension; iterated function system; Mahler function; self-affine set
- Identifier
- http://hdl.handle.net/1959.13/1436704
- Identifier
- uon:40110
- Identifier
- ISSN:1530-7638
- Language
- eng
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