GEOMETRIC MODELING OF FRACTAL STRUCTURED OBJECTS BASED

What is it about?

The article offers suggestions about mathematical modeling of architectural objects based on the functional image using the constructive operations of the theory of R-functions. Given in 2D format 3D surface from the data equations work exit according to approach offer done. Work developed mathematician from the model using construction - architecture L-systems in objects based on three measured geometric to the object processing to give through fractal 3D computer design of an architectural building model work developed. In the article work developed samples of the method opportunities reflection made. Fractal geometry terminology and concepts using natural surfaces, forms enough level right, good quality and quantitative way described. In architecture forms structure spatial organize to be done fractal geometry using natural structures like enough level description possible has been repetitive to himself similar from structures use, fractal construction the rules mathematician models and computer graphics using in architecture application this direction possibilities efficiency increases.

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Photo by Karim MANJRA on Unsplash

Photo by Karim MANJRA on Unsplash

Why is it important?

The system of self-similar hierarchical forms is one of the most important geometric principles for building an architectural composition. B.Mandelbrot, who discovered fractal algorithms in nature and human creation, defines self-similarity as follows: “If each part of the shape resembles the overall geometry, the shape and construction steps are also similar” [1]. To study fractals, we need to divide them into specific classes. Several types of fractals can be found in nature: geometric fractals, algebraic fractals and stochastic fractals [3]. A fractal is a geometric shape that repeats over and over again, changing the size of certain parts. In other words, if you zoom in and look at a small part of the fractal shape, it looks like a larger part or whole shape of the picture. Moreover, in the case of fractals, increasing scale does not mean simplifying their structure. So in all cases we see the same composite. As geometric objects, fractals generally have the following properties: 1. Self-similarity. In the simplest case, a small part of the fractal contains all the information about the fractal. 2. Fractional. The fractal of a fractal is a mathematical expression of the magnitude of a fractal error. 3. Irregularity. If you define a fractal function in mathematical terms, an irregular function is non-flat and non-differentiable at any point. 4. Scaling. a. Ability to develop (principle of continuous formation). b. Metric measurement using fractions (principle of dimensional equality). c. Principle of Boundary Uncertainty (Edge Uncertainty). d. Dynamic Chaos Principle. 5. Fractal dimension is a non-integer dimension introduced by Benoit Mandelbrot [1]. Architectural structures may not always be properly described in the language of traditional Euclidean geometry. Because they contain different forms. Therefore, the terminology and concepts of fractal geometry topology are used to analyze them. Such a scientific approach helps to determine the general characteristics of the structure of forms in nature, the similarities and differences of natural and architectural morphogenesis. These approaches, which lead to the implementation of single principles of formation in nature, have already been used in the analysis of architectural forms [4-5], but they have not yet been sufficiently developed and clarified. Computer Models of Architectural Projects Based on Factual Geometry Digital modeling techniques play an important role in helping designers with conceptual architectural projects. A modeling system using a computer can generate various images in the initial design stage, contributing to the search for alternative architectural forms. Currently, various design approaches are used in the formation of architectural products. The proposed approach is evaluated as a creative tool in architectural design. Buildings, spaces, surrounding environments, and symbols of this society, which are the subjects of architecture, are also elements of object language that form relationships based on fractal geometry. This relationship can be analyzed through principles based on fractal geometry.

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