4 papers
Hausdorff measure of cartesian product of Cantor sets
Siyuan Guo, Taylor Jones
Hausdorff measure and Hausdorff dimension are useful tools to describe fractals. This paper investigates the bounds on the -dimensional Hausdorff measure of the -fold…
Random subsets of Cantor sets generated by trees of coin flips
Pieter Allaart, Taylor Jones
We introduce a natural way to construct a random subset of a homogeneous Cantor set in via random labelings of an infinite -ary tree, where . The Cantor set…
Box-counting dimension and differentiability of box-like statistically self-affine functions
Pieter Allaart, Taylor Jones
We consider a class of "box-like" statistically self-affine functions, and compute the almost-sure box-counting dimension of their graphs. Furthermore, we consider the differentiab…
On the existence of numbers with matching continued fraction and decimal expansions
Pieter Allaart, Stephen Jackson, Taylor Jones +1
A Trott number is a number whose continued fraction expansion is equal to its base expansion for a given base , in the following sense: If ,…