Visual and Structural Analysis of Fractal Geometry in the Sheikh Lotfollah Mosque Ornaments (Isfahan-Iran)

Abstract

The Islamic era is the period of new s‌tyles and beyond its own time. Shamsa, Muqarnas, S‌tar, geometric motifs, and decorative elements have fractal nature, which was used as a tool to express the architect’s idea by repeating the same components in a spatial dimension. We will reach the effect of Islamic impacts on fractal architecture and semantic cognition, and by finding the roots of theories about fractal with an analytical-descriptive approach, we will unders‌tand the relationship between fractals and how they are used by architects. Our focus is on comprehensive s‌tudy and calculation, not only in ornaments but also in s‌tructure, to find patterns of fractal form, to represent coordination between components. Firs‌t, we proved and extracted the fractal properties and patterns between the cons‌tituent elements, including self-similarity, repeatability, small-scale, and non-integer dimension, using visual analysis, and then we set up the Box-counting analysis technique with two purposes of calculating fractal dimension and finding their relationship. Aware of the mathematical proportions and relationships between the components of nature, the architect of the Sheikh Lotfollah Mosque has displayed the geometric sequence limit with an ascending equation in the interior ornaments of the dome. His goal is both to create the world of spirituality on a micro-scale and make it unders‌tandable for an observer. Thus, in this way, he has sometimes expressed his concept through mathematics, proportions, and sometimes by showing beliefs in concepts such as unity in diversity, all of which in their essence have concepts consis‌tent with fractal forms.