We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets
The properties of self-similar sets are discussed and a brief historical survey of ideas related to ...
In this article a collection of random self-similar fractal dendrites is constructed, and their Haus...
Let K and mu be the self-similar set and the self-similar measure associated with an IFS (iterated f...
We survey some recent results on the dimension of orthogonal projections of self-similar sets and of...
We introduce a technique that uses projection properties of fractal percolation to establish dimensi...
We study the geometric properties of random multiplicative cascade measures defined on self-similar ...
A contractive similarity is a function which preserves the geometry of a object but shrinks it down ...
AbstractWe have given several necessary and sufficient conditions for statistically self-similar set...
Abstract We characterize the existence of certain geometric configurations in the fractal percolati...
Abstract. In this paper we study the radial projection and the orthogonal projection of the random C...
We prove preservation of L q dimensions (for 1 < q ≤ 2) under all orthogonal projections for a class...
Abstract. The purpose of this note is to calculate the almost sure Hausdorff dimension of uniformly ...
We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some result...
Abstract. We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (cons...
Abstract We derive an upper bound for the Assouad dimension of visible parts of self-similar sets g...
The properties of self-similar sets are discussed and a brief historical survey of ideas related to ...
In this article a collection of random self-similar fractal dendrites is constructed, and their Haus...
Let K and mu be the self-similar set and the self-similar measure associated with an IFS (iterated f...
We survey some recent results on the dimension of orthogonal projections of self-similar sets and of...
We introduce a technique that uses projection properties of fractal percolation to establish dimensi...
We study the geometric properties of random multiplicative cascade measures defined on self-similar ...
A contractive similarity is a function which preserves the geometry of a object but shrinks it down ...
AbstractWe have given several necessary and sufficient conditions for statistically self-similar set...
Abstract We characterize the existence of certain geometric configurations in the fractal percolati...
Abstract. In this paper we study the radial projection and the orthogonal projection of the random C...
We prove preservation of L q dimensions (for 1 < q ≤ 2) under all orthogonal projections for a class...
Abstract. The purpose of this note is to calculate the almost sure Hausdorff dimension of uniformly ...
We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some result...
Abstract. We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (cons...
Abstract We derive an upper bound for the Assouad dimension of visible parts of self-similar sets g...
The properties of self-similar sets are discussed and a brief historical survey of ideas related to ...
In this article a collection of random self-similar fractal dendrites is constructed, and their Haus...
Let K and mu be the self-similar set and the self-similar measure associated with an IFS (iterated f...
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