Statistically self-affine sets: Hausdorff and box dimensions

Dimensions of random affine code tree fractals

“…In this case no non-trivial upper bound for the contraction ratios is needed in the analogue of the result of Falconer [9] and Solomyak [24]. Gatzouras and Lalley [15] investigated random counterparts of self-affine Bedford-McMullen carpets. In their model the linear parts of the affine mappings are nonrandom, but the translation vectors and the number of maps are independently, randomly chosen at every step of the construction.…”

“…In [13,15,17] the randomness is quite strong in the sense that there is total independence both in space, that is, between different nodes at a fixed construction level, and in scale or time, that is, once a node is chosen, its descendants are selected independently of the previous history. We will consider probability distributions which have certain independence only in time direction, more precisely, there exists almost surely an infinite sequence of neck levels N n where all the sub code trees starting from level N n are the same and the events depending only on the construction before a neck level N k are independent of those depending only on the construction after N k .…”

A Class of Random Cantor Sets

“…There exists a huge literature on computing the 'almost sure' dimensions for many other random fractal sets. We refer to [6,7,11,14,17,26,29] and reference therein. For the general estimations and the almost sure dimensions of these random Cantor sets, we have the following result.…”

Hausdorff Dimension of Certain Random Self-Affine Fractals

“…There are some previous works on the Hausdorff dimension of randomly generated fractals in the non-conformal setting, namely [6] and [8] . These works deal with random general Sierpinski carpets, while the present work deals with random self-affine carpets.…”