An Effective Method for Compute the Roughness of Fractal Facades Based on Box-Counting Dimension (Db)

Abstract

Benoit Mandelbrot coined the word “fractal” in the late 1970s, but an object is now defined as fractals in form known to artists and mathematicians for centuries. A fractal object is self-similar in that the subsections of the object are somewhat similar to the whole object. No matter how small the subdivision is, the subsection contains no less detail than the whole. Atypical example of a fractal body is the “snowflake curve” (invented by Helga von Koch (1870-1924) in 1904. There are as many relationships between architecture, the arts, and mathematics as symmetry. The golden ratio, the Fibonacci sequence in this paper explain the method of counting box and measuring the roughness ratio. And small scale analysis after calculating the box to understand fractal concepts, we must know two dimensions. Through analyzing the samples in the research, it has been proven that fractal geometry is present everywhere in our lives in nature, in buildings, and even in plants and its role in architecture is to find fractal systems that appeal to our inclinations for dynamic vitality. Therefore, finding such fractals enables us to create high-performance structures that achieve psychological, aesthetic and environmental aspects in an integrated design. Therefore, Self- Similarity Dimension (Ds) Box-counting Dimension (Db.) All of these dimensions are directly related to the fractional dimension of Mandelbrot (D). In all similar constructions there is a relationship between the scale factor and the number of the smaller pieces the original construction is divided into.