Fractals In Three-Dimensional Space. I-Fractals

It has long been known that there are fractals, which construction resolve into cutting out of elements from lines, curves or geometric shapes according to a certain law. If the fractal is completely self-similar, its dimensionality is reduced relative to the original object and usually becomes fractional. The whole fractal is often decomposing into a set of separate elements, organized in the space of corresponding dimension. German mathematician Georg Cantor was among the first to propose such fractal set in the late 19th century. Later in the early 20th century polish mathematician Vaclav Sierpinski described the Sierpinski carpet – one of the variants for the Cantor set generalization onto a two-dimensional space. At a later date the Austrian Karl Menger created a three-dimensional analogue of the Sierpinski fractal. Similar sets differ in a number of parameters from other fractals, and therefore must be considered separately. In this paper it has been proposed to call these fractals as i-fractals (from the Latin interfican – cut). The emphasis is on the three-dimensional i-fractals, created based on the Cantor and Sierpinski principles and other fractal dependencies. Mathematics of spatial fractal sets is very difficult to understand, therefore, were used computer models developed in the three-dimensional modeling software SolidWorks and COMPASS, the obtained data were processing using mathematical programs. Using fractal principles it is possible to create a large number of i-fractals’ three dimensional models therefore important research objectives include such objects’ classification development. In addition, were analyzed i-fractals’ geometry features, and proposed general principles for their creation.