Happy Pi Day 2024! In this video, I attempt to create an Apollonian Gasket using the Descartes Circle Theorem and complex numbers. So many circles! Code: https://thecodingtrain.com/challenges...

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p5.js Web Editor Sketches:
🕹️ Apollonian Gasket: https://editor.p5js.org/codingtrain/s...
🕹️ Colorful Recursive Gaskets in Gaskets: https://editor.p5js.org/codingtrain/s...

🎥 Previous:    • Coding Challenge 181: Weighted Vorono...  
🎥 All:    • Coding Challenges  

References:
🔗 Apollonian Gasket: https://en.wikipedia.org/wiki/Apollon...
🔗 A Tisket, a Tasket, an Apollonian Gasket: https://www.americanscientist.org/art...
🔗 Apollonian Gaskets: https://mathlesstraveled.com/2016/04/...
🔗 Beyond the Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf
🔗 The Kiss Precise: https://www.nature.com/articles/13710...
🔗 Frederick Soddy: https://en.wikipedia.org/wiki/Frederi...
🔗 Problem of Apollonius: https://en.wikipedia.org/wiki/Problem...
🔗 Four Proofs of a Generalization of the Descartes Circle Theorem: https://www.jstor.org/stable/2316373
🔗 Beyond the Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf
🔗 Descartes' theorem: https://en.wikipedia.org/wiki/Descart...
🔗 Complex.js: https://www.npmjs.com/package/complex.js

Related Coding Challenges:
🚂 21 Mandelbrot Set with p5.js:    • Coding Challenge #21: Mandelbrot Set ...  
🚂 22 Julia Set in Processing:    • Coding Challenge #22: Julia Set in Pr...  
🚂 77 Recursion:    • Coding Challenge #77: Recursion  
🚂 50 Circle Packing:    • Coding Challenge #50.1: Animated Circ...  
🚂 95 Approximating the Value of Pi:    • Coding Challenge 95: Approximating th...  
🚂 96 Visualizing the Digits of Pi:    • Coding Challenge #96: Visualizing the...  
🚂 97 The Book of Pi:    • Coding Challenge #97: The Book of Pi ...  
🚂 139 Calculating Digits of Pi with Collisions:    • Coding Challenge #139: Calculating Di...  
🚂 140 Leibniz Formula for Pi:    • Coding Challenge #140: Pi Approximati...  
🚂 141 Calculating Digits of Pi with Mandelbrot Set:    • Coding Challenge #141: Calculating Di...  
🚂 169 Pi in the Sky Game:    • Coding Challenge 169: Pi in the Sky Game  
🚂 176 Buffon's Needle:    • Coding Challenge 176: Buffon's Needle  

Timestamps:
0:00 Happy PI Day!!
1:40 References
3:22 Describe the Apollonian problem
5:51 Curvature
10:08 Start coding!
11:53 Write a function to find the fourth curvature
15:31 Complex numbers
21:11 Create a complex number class
22:52 Square root of -1
25:32 Square root of a complex number
27:57 Implement complex Descartes theorem
33:50 Make the circles in the complexDescartes function
36:26 Use an array to add recursion
41:04 Validate the circles
42:35 Check if all 4 circles are tangent
48:04 Stop adding circles when radius falls below a threshold
49:20 Implement arbirtary arrangement of circles
53:14 Debug
55:32 Possible variations
56:34 Outro

Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound

🚂 Website: https://thecodingtrain.com/
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🎥 Coding Challenges:    • Coding Challenges  
🎥 Intro to Programming:    • Start learning here!  

🔗 p5.js: https://p5js.org
🔗 p5.js Web Editor: https://editor.p5js.org/
🔗 Processing: https://processing.org

📄 Code of Conduct: https://github.com/CodingTrain/Code-o...

This description was auto-generated. If you see a problem, please open an issue: https://github.com/CodingTrain/thecod...

#apolloniangasket #pi #circlepacking #complexnumbers #curvature #descartestheorem #p5js #javascript
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