Random soups, carpets and fractal dimensions

Random soups, carpets and fractal dimensions

We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and equal to their expectation dimension. We also estimate their low-intensity limiting behavior. This applies in particular to the “conformal loop en...

View from the Pennines: Ten Martinis and Fractal Carpets

Some insects are living in my children’s sand pit. I don’t know what they are and I don’t know where they are, but without question they are in there. If the sand pit has not been used for a few days the surface of the sand is covered by small tracks. The movement of the insects smooths the larger hills and castles, and the visual effect of the trails, give or take considerations of colour, is ...

FONT DISCRIMINATIO USING FRACTAL DIMENSIONS

One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dime...

Fractal dimensions

Random Walks on Graphical Sierpinski Carpets

We consider random walks on a class of graphs derived from Sierpinski carpets. We obtain upper and lower bounds (which are non-Gaussian) on the transition probabilities which are, up to constants, the best possible. We also extend some classical Sobolev and Poincar e inequalities to this setting.