Apollonian Gasket

The Apollonian gasket is like a super cool picture made of circles. It starts with three circles that are all touching each other, like friends hugging! Then, you draw a new circle in the tiny space between them.

This new circle also touches the first three. You can keep adding more and more circles, and each new circle fits perfectly into a small gap, touching three other circles. It’s like a never-ending game of fitting shapes together!

This amazing pattern is named after a very smart person from a long, long time ago named Apollonius of Perga. He was a mathematician, which means he loved numbers and shapes. He lived in ancient Greece, where people built amazing buildings and thought about the world in clever ways.

Even though he lived thousands of years ago, his ideas about circles still make beautiful patterns today. It’s like a secret code he left for us to discover!

These circles are special because they create a pattern that looks the same no matter how close you zoom in. It’s called a fractal! Imagine looking at a snowflake; it has tiny parts that look like the whole snowflake.

The Apollonian gasket is like that, but with circles. This kind of pattern is found in nature, like in the branches of trees or the shape of a lightning bolt. It shows us how simple rules can create very complex and beautiful things.

Making an Apollonian gasket is like a fun challenge. You start with three circles that are all touching each other. Then, you find the little empty space in the middle.

You draw a new circle that fits perfectly in that space, touching all three of the first circles. Now you have four circles! You can do this again and again.

Find the new tiny spaces between the circles and draw even smaller circles that touch three others. You can keep going forever, making more and more circles!