Fraktala
Ena fika, na fraktala e dua na buila veijiometri e tiko kina na ituvatuva matailalai ena veivakatautauvatataki lailai, e dau tiko kina e dua na ivakarau ni fractal e sivia sara na ivakarau ni topological. E vuqa na fractals e laurai tautauvata ena veimataqali ivakarau, me vaka e vakaraitaka na veivakatorocaketaki veitaravi ni Mandelbrot seti.[1][2][3][4] Na vakaraitaki oqo ni ivakarau tautauvata ena vakalevutaki ni veivakatautauvatataki lailai e vakatokai na tautauvata vakataki koya, kilai talega me vakarabailevutaki ni veivakatautauvatataki se veivakatautauvatataki ni veivakatautauvatataki; kevaka e tautauvata sara ga na veivakatautauvatataki oqo ena veivakatautauvatataki kecega, me vaka ena vutovuto Menger, na ibulibuli e vakatokai me affine vakataki koya-tautauvata.[5] Na jiometri fraktala e tiko ena loma ni tabana ni fika ni icavacava ituvatuva.
E dua na sala e duidui kina na fraktala mai na iwiliwili ni veijiometri vakaiyalayala na sala era vakarautaka kina. Na vakaruataki ni balavu ni bati ni dua na polikoni vakasinaiti e vakalevutaka na kena vanua ena va, ka sa rua (na ratio ni vou ki na balavu ni yasana makawa) laveti cake ki na kaukauwa ni rua (na ivakarau tudei ni polygon vakasinaiti). Vakakina, kevaka e vakaruataki na radiusi ni dua na vuravura vakasinaiti, na kena iwiliwili e vakalevutaki ena walu, ka sa rua (na raitio ni radiusi vou ki na radiusi makawa) ki na kaukauwa ni tolu (na ivakarau tudei ni vuravura vakasinaiti). Ia, kevaka e dua na fractal ni dua-na-ivakarau ni balavu e vakaruataki kece, na itukutuku ni vanua ni fractal na ivakarau ena dua na kaukauwa e sega ni dodonu me dua na taucoko ka sa raraba levu cake mai na kena ivakarau ni ivakarau. Na kaukauwa oqo e vakatokai na ivakarau ni fraktala ni ka veijiometri, me vakaduiduitaka mai na ivakarau ni ivakarau (ka sa vakatokai vakamatanitu na ivakarau veitopolji).[6]
Veitikina
[veisau | edit source]- ↑ Mandelbrot, Benoît B. (1983). The fractal geometry of nature. Macmillan. ISBN 978-0-7167-1186-5.
- ↑ Falconer, Kenneth (2003). Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons. xxv. ISBN 978-0-470-84862-3.
- ↑ Briggs, John (1992). Fractals:The Patterns of Chaos. London: Thames and Hudson. p. 148. ISBN 978-0-500-27693-8.
- ↑ Vicsek, Tamás (1992). Fractal growth phenomena. Singapore/New Jersey: World Scientific. pp. 31, 139–146. ISBN 978-981-02-0668-0.
- ↑ Gouyet, Jean-François (1996). Physics and fractal structures. Paris/New York: Masson Springer. ISBN 978-0-387-94153-0.
- ↑ Mandelbrot, Benoît B. (2004). Fractals and Chaos. Berlin: Springer. p. 38. ISBN 978-0-387-20158-0.
A fractal set is one for which the fractal (Hausdorff-Besicovitch) dimension strictly exceeds the topological dimension