Rohan Senapati
Class of 2027Dublin, California
About
Hello! My name is Rohan Senapati, and I worked with Polygence to explore the depths of fractal geometry. From a young age, I have been interested in competitive mathematics. Recently, as I was working through a problem set, I came across the field of complex numbers, and its intricacies truly fascinated me. After working through many problems regarding complex numbers and gaining intution, I narrowed my interest down to the Mandelbrot set. My passion drove me to derive and prove various properties of the Mandelbrot set, some of which have yet to be documented in literature. This project not only deepened my understanding of complex dynamics and fractals, but it also fueled my passion for mathematical discovery. Besides theoretical problems, fractals have real-world applications today, such as cryptography. Their complex patterns can be used to create more secure encryption systems, which is central to cybersecurity. As I move forward, I am hoping to apply my knowledge to practical applications in the field of dynamical systems, and contribute to the broader field of computational mathematics.Projects
- "A Geometric Exploration of Generalized Mandelbrot Sets" with mentor Jason (Mar. 16, 2025)
Project Portfolio
A Geometric Exploration of Generalized Mandelbrot Sets
Started May 28, 2024
Abstract or project description
The exploration of Mandelbrot sets offers readers an insightful look into the deep and elegant connections between complex numbers and geometry. By plotting Mandelbrot sets and running simulations using tools like matplotlib and googleColab, the data has be useful for aiding me in deriving conjectures, and the tools I gained over the course of the project by continuously solving problems, has been invaluable for proving these conjectures. Interesting properties analyzed from the data include graphical relationships between jth degree polynomials of the form f(z) = z^j + c and area approximations, along with the investigation of relationships between degree and petals, and various symmetries. By running simulations, and deriving and proving various conjectures, my research contributes to the field of complex dynamics by tackling open problems regarding mandelbrot sets.