Застосування фракталів для створення 3d комп'ютерної графіки в кінематографі

Abstract

The paper investigates how fractal geometry is used to create three dimensional graphics in filmmaking. Mandelbrot’s theoretical framework - self similarity and Hausdorff dimension - is reviewed as the mathematical basis. Three core production algorithms are examined: L-systems for plant and vegetation modeling, Perlin noise for terrain and texture synthesis, and ray marching for volumetric 3D fractal rendering. The timeline from Loren Carpenter’s Vol Libre (1980) through Star Trek II: The Wrath of Khan (1982) to contemporary blockbusters illustrates how deeply fractal methods are embedded in modern CGI pipelines.