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  • 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