Fractal Aesthetics in Architecture
Journal Paper, in Applied Mathematics & Information Sciences (AMIS)
Wolfgang E. Lorenz, Jan Andres und Georg Franck
Keywords: Architectural analysis, design analysis, fractal geometry,
complexity, harmonic proportion, construct/constituent pairing, box-counting.
June, 2017, Vienna & Olomouce
This paper deals with fractal aesthetics and proposes a new fractal analysis method for the perceptual study of architecture. The authors believe in the universality of formulas and aim to complement the architectural description in terms of proportion. Although a well established fractal analysis method to describe the complexity of facades across different scales already exists, box-counting is imprecise because of too many in?uences coming along with the method itself. The authors consider the self-similarity as an important part of aesthetic quality in architecture. This is due to the fact that it describes a concept of consistency that holds everything together from the whole to the smallest detail which refers to the classical meaning of the word symmetry. Hence, a new fractal analysis method is introduced which so far has been applied to quantitative linguistics. Basically, elements of different order, called construct/constituent pairs, are counted and related in a formula. In architecture the pairing consists of likewise elements belonging to different orders, from the overview, the fundamental elements to the smaller details. As a conjecture, some preferable fractal dimensions (from the aesthetical point of view) are proposed for architectural structures.