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