Abstract:
We consider configurations of lines of curvilinear three-web that can be inscribed in a triangle formed by the lines of this web. In case the inscribed configuration is triangulating, it generates a fractal in each such triangle. This allows us to associate with smooth function of two variables a certain fractal that generalizes the well-known Sierpiński triangle. We introduce the concept of a regular fractal and prove that a regular fractal is obtained only for a regular three-web (generalization of the basic theorem on hexagonal three-webs). We also find the fractal dimensions of some regular fractals and formulate problems related to fractal dimension.
Keywords:three-web, three-web configuration, inscribed configuration, triangulating configuration, fractal associated with a three-web, generalized Sierpińsky triangle.
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