Apollonian Gasket Fractal - A Mesmerizing Mathematical Visualization

The Apollonian Gasket Fractal is a captivating visualization of a classical mathematical concept in computational geometry. This project implements an interactive and customizable fractal generator that creates beautiful, intricate patterns based on the principle of circle packing. Users can manipulate various parameters to explore different fractal iterations and see the mathematical beauty unfold in real-time.

Development Highlights

This project showcases the intersection of mathematics, computer graphics, and interactive design:

• Implemented a recursive algorithm to generate Apollonian Gasket fractals with customizable depth levels using C# in Unity.
• Created an efficient circle generation system that calculates tangent circles using Descartes' theorem and proper coordinate mapping.
• Designed an intuitive user interface that allows real-time parameter adjustments, including recursion depth, initial circle configurations, and color schemes.
• Optimized performance to handle high recursion depths without compromising framerate or visual quality in 2D Sprites & LineRenderer .
• Added screenshot functionality to capture high-resolution images of particularly interesting fractal configurations.
• Explored advanced rendering techniques to enhance the visual appeal of the mathematical patterns.
• Created an educational component that explains the mathematical principles behind Apollonian Gaskets.
• Developed both desktop and mobile versions to make this mathematical art accessible across different platforms.