A new matrix potential game for self-affine sets yields non-empty intersections, Hausdorff dimension lower bounds, and finite-pattern theorems for classes of carpets with zero thickness.
Falconer.Fractal geometry - mathematical foundations and applications.John Wiley & Sons, Ltd., Chichester, 1990
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The matrix potential game and structures of self-affine sets
A new matrix potential game for self-affine sets yields non-empty intersections, Hausdorff dimension lower bounds, and finite-pattern theorems for classes of carpets with zero thickness.