Комбінаторні конфігурації, фрактали, фрактальна розмірність комбінаторних множин: Fìz.-mat. model. ìnf. tehnol. 2021, 33:170-174
Combinatorial configurations and their sets are considered. The definitions of these objects are given, recurrent combinatorial operators are introduced, with the help of which they are formed, and rules are formulated according to which their sets are ordered. The property of periodicity, which tak...
Збережено в:
| Дата: | 2021 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2021
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| Теми: | |
| Онлайн доступ: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/223 |
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| Назва журналу: | Physico-mathematical modeling and informational technologies |
Репозитарії
Physico-mathematical modeling and informational technologies| Резюме: | Combinatorial configurations and their sets are considered. The definitions of these objects are given, recurrent combinatorial operators are introduced, with the help of which they are formed, and rules are formulated according to which their sets are ordered. The property of periodicity, which takes place in the generation of combinatorial configurations, is described. It follows from the recurrent way of their formation and ordering. The fractal structure of combinatorial sets is formed due to the described rules, in which the property of periodicity is used. Analysis of these structures shows that they are self-similar, both finite and infinite, which is characteristic of fractals. Their fractal dimension is introduced, which follows from the rules of generating combinatorial configurations and corresponds to the number of these objects in their set.
References
Lypskyi, V. (1988). Kombinatorika dlija prohrammistov. Per. s polsk. M.: Mir. (in Russian).
Sachkov, V. N. (1977). Kombinatornyje metody dickretno’j matematiki. М.: Nauka. (in Russian).
Tymofijeva, N. K. (2015). Znakovi kombinatorni prostory ta shtuchy’j intelekt Shtuchny`j intelekt, 1-2(67-68), 180–189.
Tymofijeva, N. K. (2007). Teoretyko-chyslovi metody rozviazannia zadach kombinatornoi optymizatsii: avtoref. dys. dokt. tekhn. nauk: 01.05.02. Kyiv: ІK іm. V.M. Gluchkova NАN Ukrainy.
Mandelbrot, B. (2010). Fraktalnaja geometrija prirody. Ishevsk: NITS «Reguljartaja i xaotuthesraja dinamika».
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| DOI: | 10.15407/fmmit2021.33.170 |