Topic of Research Seminar: Principles of Fractal Geometry and its Applications

Abstract: Fractal geometry, introduced by Benoit Mandelbrot in 1975, describes complex, self-similar patterns found in nature and mathematics. Unlike traditional geometry, fractals exhibit non-integer dimensions and infinite detail, allowing accurate modeling of irregular phenomena. Key properties include self-similarity (exact, quasi, and statistical) and measurable fractal dimensions like Hausdorff and box-counting dimensions. The presentation highlights significant examples: Iterated Function System (IFS) fractals such as the Sierpinski Triangle and Koch Curve, and complex number fractals like the Mandelbrot set and Julia set. These fractals demonstrate how simple mathematical rules can generate infinitely intricate structures. Fractal geometry has broad applications, including computer graphics (image compression and realistic landscapes), fluid mechanics (modeling turbulent flows), and telecommunications (designing compact, efficient antennas). In essence, fractal geometry provides a powerful tool to analyze and represent the complexity of natural and artificial systems, bridging the gap between mathematics, science, and technology.

Subject Field of Topic: Measure Theory

Name of Speaker: Mr. Furqan Nazeer

Professorial Rank of Speaker: PhD Scholar (Mathematics Dpt.), School of Natural Sciences (SNS – NUST)

Email of Speaker: [email protected]

Affiliation of Speaker: School of Natural Sciences (SNS – NUST)

Date and Venue: (Wednesday) 18 December 2024, 1530 hrs, CR # 202, New Building SNS, School of Natural Sciences, NUST Islamabad