The Apollonian gasket is a fractal formed by a process of recursively packing circles within a larger circle, leaving no space between them. It is named after the ancient Greek philosopher Apollonius of Perga. The study of this fractal, as well as other fractals, raises several philosophical questions and has implications in different branches of philosophy, including metaphysics, epistemology, and aesthetics.

Metaphysics: The Apollonian gasket fractal raises questions about the nature of reality and the relationship between mathematics and the physical world. Fractals display self-similarity at different scales, suggesting that the patterns governing the universe might be repetitive or recursive. This raises questions about the nature of space and time, and whether there is an inherent structure to the cosmos.
Epistemology: Fractals like the Apollonian gasket challenge our understanding of knowledge and the limits of human comprehension. They demonstrate the complexity that can emerge from simple mathematical rules and question our ability to understand the full scope of reality. The study of fractals may also inform the development of new scientific methods and paradigms.
Aesthetics: The Apollonian gasket and other fractals possess an inherent beauty, which raises questions about the nature of art and aesthetic appreciation. The recursive patterns found in fractals can inspire both visual and mathematical artists, leading to a fusion of art and science. The connection between mathematical structures and aesthetic experience raises questions about the universality of beauty and the role of mathematics in art.
Ethics: The study of fractals can lead to a greater appreciation of the interconnectedness and complexity of the natural world. This may influence ethical considerations, as it highlights the delicate balance of ecosystems and the potential impact of human actions on the environment.
Philosophy of mathematics: Fractals like the Apollonian gasket raise questions about the nature of mathematical objects and the relationship between mathematical abstraction and the physical world. They also highlight the power of infinity and the limits of human intuition in comprehending infinite processes.