GENERATING SIERPINSKI FRACTALS USING THE PYTHON PROGRAMMING LANGUAGE
Abstract
Starting from the basic concepts of fractals in the introduction, the paper describes the theoretical foundation of fractals, which encompasses their history, fractal dimension, classification of fractals, and methods for their generation. Practical applications are demonstrated, and the fractal phenomenon in nature, as well as the use of fractals in computer graphics, is analyzed. The methodology and tools used in the research include the Python programming language and Google Colab. Sierpinski triangle, carpet, and Menger sponge are generated, and the results are presented with a comparative analysis of the outcomes. Based on the conducted research and obtained results, it is concluded that complex shapes, such as fractals, can be generated with the help of computer graphics methods.
References
[2] Michael Frame, Amelia Urry, Fractal Worlds, Grown, Built, and Imagined, Yale university press, New Haven and London (2016);
[3] Benoit B. Mandelbrot, The Fractal Geometry of nature, W.H. Freeman and company, New York (1977);
[4] Aleksandra Ivković, Fraktalna geometrija Koch-ove krive, Univerzitet u Novom Sadu, Prirodno-matematicki fakultet, Departman za matematiku i informatiku (2019);
[5] https://www.scitepress.org/Papers/2020/104624/104624.pdf (pristupljeno u oktobru 2023.)
[6] Karuna Sangam, Homeomorphisms of the Sierpinski carpet, Bard College, Annandale-on-Hudson, New York (2018);
[7] Antonijo Sabljak, Klasični fraktali, Sveučilište J. J. Strossmayera u Osijeku, Osijek (2018);
