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  • Generations of the fractal structures

    Fractal geometry is used in the development of new designs based on the principles of fractal shaping and the study of generations of fractal structures. The structure generation is characterized by optimization of the original geometry in the process of iteration. Fractal structures of older generations have the best indicators of reliability. The aim of the study is to develop an algorithm for modeling new designs based on the principles of fractal shaping. The development of fractal structures requires the creation of new technologies and materials.

    Keywords: fractal structure, generations, fractal geometry, shaping, self-developing structures, unique structures, 3D modeling

  • The fractal Mandelbrot set and the shaping of the 3D fractal

    The theory of fractals is applicable for creating the real objects and for constructing the independent elements of the framework or the whole structure of the building. Innovative program was developed to research the shaping of the 3D fractal. The object of the study is 3D Mandelbrot fractal. External structures of various powers of 3D fractal were modeled and researched. New terminology has been developed which can be applied to 3D fractals. The power factor shows the ratio of the work of external forces to the total external. The concept of forming 3D fractal can be used in the design of unique buildings and structures.

    Keywords: fractal, fractal geometry, Mandelbrot set, volumetric fractal, fractal structure, finite element method.

  • The paradigm of fractal structures

    The article describes the basic concepts of the three-dimensional analogue of Mandelbrot set and fractal architecture. The ideas of fractal structure shaping in the process of parametric and fractal design are outlined. The algorithm for fractals visualizing in geometric forms is proposed, implemented in the program "3D fractal modeling", developed by the authors. The complex fractal structure of the three-dimensional Mandelbrot fractal is examined layer by layer and compared with the Buddhist mandalas and the architecture of the pagodas.

    Keywords: fractal, fractal geometry, Mandelbrot set, volumetric fractal , three-dimensional Mandelbrot fractal modeling, fractal structure,

  • Fractals' modeling

    The paper presents a classification of two-dimensional as well as three-dimensional fractals, fractal characteristics, methods for modeling fractals. The algorithm of visualization fractals have used in the "3D simulation of fractals" software for the first time. The points’ generator module unites the points of space into a set of triangular finite elements in the environment of the computing complex SCAD. Complex fractal geometry have transformed into a spatial finite element model of the fractal.

    Keywords: fractal, non-Euclidean geometry, fractal characteristics, two-dimensional fractals, three- dimensional fractals, 3D modeling fractal, energy of fractal, iterations of modeling fractals