Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 18, Iss. 4, October, 2014, pp. 435-463
@2014 Society for Chaos Theory in Psychology & Life Sciences


Fractional Brownian Functions as Mathematical Models of Natural Rhythm in Architecture

Ivana M. Cirovic, Business Technical College of Vocational Studies, Uzice, Serbia

Abstract: Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.

Keywords: fractals, analogy, structural alignment, rhythm, architecture