A first attempt to fractal mosaics

Thäle, Christoph

In: European congress of stereology and image analysis, ECS10, 2009, no. 10, p. 342-348

A new model for random tessellations having a fractal component is introduced. An explicit formula for the Hausdorff dimension is given and the exact gauge function of its Hausdorff measure is calculated. Moreover, fractal curvatures and mean fractal curvatures are considered. A theoretical result about the relation of these quantities is shown and is demonstrated numerically by an example. Plus

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    Summary
    A new model for random tessellations having a fractal component is introduced. An explicit formula for the Hausdorff dimension is given and the exact gauge function of its Hausdorff measure is calculated. Moreover, fractal curvatures and mean fractal curvatures are considered. A theoretical result about the relation of these quantities is shown and is demonstrated numerically by an example.