Laszlo Balazs

FRACTAL BEHAVIOR OF TREE-LIKE NICKEL AND COBALT ELECTRODEPOSITS

Fractal dimensions (exterior Minkowski-Bouligand and box dimensions) for nickel and cobalt metal trees (electrodeposits) were determined. These trees usually exhibit fractal characteristic in the 30–1000 micrometer range with fractal dimensions strongly depending on the initial metal-ion concentration of the electrolyte.

FRACTAL ANALYSIS OF ARTISTIC IMAGES: FROM CUBISM TO FRACTALISM

Black-and-white graphic images of great artists: Durer, Rembrandt, Picasso and Munch were analyzed in terms of fractal geometry. The pictures were digitized and the spatial distributions of the resulting ensembles of black and white pixels were characterized by their: (a) box dimension Db, (b) information dimension Di, and (c) mass exponent Dm. Whereas Db and Di were seen to coincide, Dm was usually found to be somewhat higher. Plates, which can best be described as line drawings, have D = 1 at small lengths, and D = 2 at length scales commensurate with that of the plate, with a fairly narrow crossover region. Some textured images, however, are of definite fractal character: their dimensions are well-defined non-integer constants over more than two orders of magnitude of length. At present the authors refrain from discussing the role of dilatation symmetry in graphic art.

CORROSION PATTERN FORMATION IN ALUMINIUM THIN LAYERS

The morphology of pitting corrosion, brought about by Cl− and Fe3+ containing acidic solutions on aluminium thin layers evaporated onto glass substrate was investigated by image analysis. The influence of electrolyte composition on the morphology was studied. In a wide range of liquid composition, patterns with uniform fractal properties were grown. The dimension of patterns was found to be between 1.9–1.97, the lower value referring to the least aggressive case. Results indicate similarities with spreading percolation processes.