Coding Challenge 182: Apollonian Gasket Fractal

TL;DR

Learn about the Apollonian Gasket fractal pattern and its mathematical properties, and create your own artistic version of the fractal using code.

Transcript

It's frozen. No. No. No. No, wait. Please, I don't want to lose all my code. [SOMBER MUSIC] Oh, god. [MUSIC PLAYING] Hi, everyone. It's Pi Day. I've been making videos to celebrate the number pi on March 14 for quite a number of years now. Typically, I'll do something where I'm trying to approximate the number of pi, or even do some kind of visuali... Read More

Key Insights

• ⭕ The Apollonian Gasket is a fractal pattern made up of circles that are mutually tangent to each other.
• ⭕ The pattern can be created through a process of recursively finding the next circle that is mutually tangent to a set of three circles.
• ⭕ The Descartes theorem is used to calculate the curvatures of the circles in the Apollonian Gasket pattern.
• ⭕ The curvatures of the circles can be positive or negative, depending on their position in relation to other circles.
• 🧘 The Apollonian Gasket pattern can be customized by varying the radius, position, and color of the circles, as well as applying different shapes or algorithms to the design.
• ❓ The Apollonian Gasket has connections to mathematics, geometry, and fractal theory.
• 👻 The pattern can be created using code, allowing for the exploration and visualization of the mathematical concepts involved.

Questions & Answers

Q: What is the Apollonian Gasket?

The Apollonian Gasket is a fractal pattern made up of circles that are mutually tangent to each other.

Q: How do you create the Apollonian Gasket pattern?

The pattern is created by recursively finding the next circle that is mutually tangent to a set of three circles.

Q: What is the Descartes theorem?

The Descartes theorem is a mathematical equation that relates the curvatures of four mutually tangent circles.

Q: How can the Apollonian Gasket pattern be customized?

The pattern can be customized by varying the radius and position of the circles, as well as adding color or other shapes to the design.

Summary & Key Takeaways

• The Apollonian Gasket is a fractal pattern made up of circles that are mutually tangent to each other.

• The pattern can be created through a process of recursively finding the next circle that is mutually tangent to a set of three circles.

• The Descartes theorem is used to calculate the curvatures of the circles in the Apollonian Gasket pattern.