Coding Challenge 182: Apollonian Gasket Fractal

Step-by-Step Tutorial: Creating an Apollonian Gasket Fractal in p5.js

1. Introduction and Setup

• Watch the video titled "Coding Challenge 182: Apollonian Gasket Fractal" by The Coding Train for an overview.
• Open your p5.js editor or online editor to follow along with the coding challenge.

2. Understanding the Apollonian Gasket

• Learn about the Apollonian Gasket, a fractal pattern involving mutually tangent circles.
• Understand the concept of curvature and its relation to circle radius.

3. Implementing the Circle Class

• Create a Circle class in your p5.js sketch to represent circles with position, radius, and curvature.
• Include functions in the Circle class to calculate distance between circles and determine if they are mutually tangent.

4. Calculating the Curvature of the Fourth Circle

• Write functions to calculate the curvature of the fourth circle given three mutually tangent circles using the Descartes theorem.

5. Generating the Apollonian Gasket

• Create an algorithm to generate a series of mutually tangent circles to form the Apollonian Gasket fractal.
• Use recursion to continue generating new circles based on existing tangent circles.

6. Visualizing the Apollonian Gasket

• Draw the circles on the canvas using p5.js functions like ellipse() to represent the Apollonian Gasket.
• Ensure that the circles are correctly positioned and visually appealing.

7. Adding Interactivity and Customization

• Add interactivity to your sketch, such as generating new gaskets on mouse click or button press.
• Experiment with color variations, different shapes, or nested gaskets for creative visual effects.

8. Testing and Optimization

• Test your code to ensure the gasket generation works smoothly and accurately.
• Optimize your code for better performance and cleaner structure.

9. Further Exploration

• Explore additional resources and papers related to the Apollonian Gasket for a deeper understanding.
• Share your creations and variations of the Apollonian Gasket with the coding community for feedback and inspiration.

10. Conclusion

• Celebrate Pi Day by creating and sharing your unique Apollonian Gasket fractal art.
• Reflect on your coding journey and the creative possibilities of fractal patterns in programming.