Two-stage modeling of a parametric architecture object of a complex parametric architecture are considered in the article. At the first stage it was analyzed the evolution of the formation of an analytical surface obtained by rotating the Lame curve in a plane perpendicular to the axis of rotation. During the investigation were considered changes in the intensity of rounding of the corners of the shape in the horizontal plane. Study of screw parametric surfaces was carried out at the second stage. New forms of a superellipse were developed to solve the problem of determining the surface of an object of parametric architecture that is resistant to aerodynamic impact. Numerical experiment with use of the finite element method in the ANSYS PC allowed to construct a new analytical surface with a different angle of twisting of floor slabs along the height of a unique building. The proposed method of research and application of the possibilities of the evolution of shaping allows to proceed to the modernization of BIM technologies in the design of unique buildings and structures.

Keywords: parametric architecture, evolution of shaping, aerodynamics, finite element method, analytical surfaces

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 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 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,

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