The Apollonian Gasket

The Apollonian Gasket is a fractal generated by repeatedly filling the gaps between three touching circles with additional circles. Starting with three circles, each time you add a new circle that fits perfectly in the space between them, the process creates a complex, infinitely detailed pattern. This mathematical structure exhibits self-similarity, meaning that small sections mirror the entire shape. The Apollonian Gasket showcases fascinating relationships between geometry, symmetry, and space, revealing how simple rules can produce intricate designs. It's a beautiful example of how mathematics can blend aesthetics and complexity.