FRAKTALLAR NAZARIYASINING ASOSIY TUSHUNCHALARI VA GEOMETRIK MODELLASHTIRISHDAGI QO‘LLANILISHI
Keywords:
fraktal, fraktal geometriya, o‘ziga-o‘xshashlik, fraktal o‘lcham, Hausdorff o‘lchami, qutilarni sanash usuli, L-tizim, Turtle grafika, IFS, geometrik modellashtirish, Mandelbrot to‘plami.Abstract
Ushbu maqolada fraktal geometriyaning shakllanish tarixi, fraktal tushunchasining mazmuni hamda fraktallarga xos bo‘lgan asosiy xususiyatlar — o‘ziga-o‘xshashlik, kasr o‘lcham (fraktal o‘lcham), nomuntazamlik va rekursiv tuzilish tahlil qilinadi. Shuningdek, fraktal tuzilishli obyektlarni analitik va algoritmik yondashuvlar yordamida modellashtirish masalalari yoritilib, L-tizimlar (Lindenmayer tizimlari), iteratsiyalangan funksiyalar tizimi (IFS) kabi klassik usullarning mohiyati bayon etiladi. Fraktallarning amaliy ahamiyati tabiiy obyektlar modeli, kompyuter grafikasi, shaharsozlik, sensor tarmoqlari, materiallar va iqtisodiy vaqt qatorlari kabi yo‘nalishlar kesimida ko‘rsatib beriladi. Maqola fraktal geometriyani murakkab shakllarni yaratish va tahlil qilishda universal matematik-axborotiy vosita sifatida asoslaydi.
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