Geodesic
On fractal constructions on curvilinear three-web
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2019), pp. 63-72

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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. 
@article{IVM_2019_9_a5,
     author = {A.M. Shelekhov},
     title = {On fractal constructions on curvilinear three-web},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--72},
     publisher = {mathdoc},
     number = {9},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_9_a5/}
}
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A.M. Shelekhov. On fractal constructions on curvilinear three-web. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2019), pp. 63-72. http://geodesic.mathdoc.fr/item/IVM_2019_9_a5/