Fractal Analysis and Aesthetic Evaluation of Geometrically Overlapping Patterns

摘要

An extended fractal dimension is introduced and applied to several figures whose fractal images are similar in a statistical sense. The box-counting method by computer-aided image analysis is adapted to measure the extended fractal dimension of patterns. When applied to an ideal fractal figure, the value measured with this method closely agrees with the theoretical value. Image information such as the number of voids and void sizes in twenty-nine different kinds of patterns is obtained by image processing. All these patterns are used as sample patterns for sensory evaluation and fractal analysis. A good correlation exists between the fractal dimension and the sensory evaluation value for beauty and complexity of patterns.