Fractals Born From Simple Tangent Circles

You can create a complex fractal by simply drawing circles inside the gaps of other circles. As you fill every tiny space with a new circle that touches three others, you create a pattern that repeats forever.

This infinite structure is known as an Apollonian gasket, named after a Greek mathematician who studied tangent circles over two millennia ago. Because every new circle must touch three existing ones, the number of circles grows exponentially as you zoom into the empty gaps. It perfectly illustrates how incredibly simple rules can generate infinite, intricate complexity. This geometric pattern is more than just art; it is a fundamental example of how fractal dimensions work in mathematics.