Coding Challenge 182: Apollonian Gasket

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: 🚀 Watch this video ad-free on Nebula Web Editor Sketches: 🕹️ Apollonian Gasket: 🕹️ Colorful Recursive Gaskets in Gaskets: 🎥 Previous: 🎥 All: References: 🔗 Apollonian Gasket: 🔗 A Tisket, a Tasket, an Apollonian Gasket: 🔗 Apollonian Gaskets: 🔗 Beyond the Descartes Circle Theorem: 🔗 The Kiss Precise: #preview 🔗 Frederick Soddy: 🔗 Problem of Apollonius: 🔗 Four Proofs of a Generalization of the Descartes Circle Theorem: 🔗 Beyond the Descartes Circle Theorem: 🔗 Descartes’ theorem: ’_theorem 🔗 : Related Coding Challenges: 🚂 21 Mandelbrot Set with : 🚂 22 Julia Set in Processing: 🚂 77 Recursion: 🚂 50 Circle Packing: 🚂 95 Approximating the Value of Pi: 🚂 96 Visualizing the Digits of Pi: 🚂 97 The Book of Pi: 🚂 139 Calculating Digits of Pi with Collisions: 🚂 140 Leibniz Formula for Pi: 🚂 141 Calculating Digits of Pi with Mandelbrot Set: 🚂 169 Pi in the Sky Game: 🚂 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: 👾 Share Your Creation! 🚩 Suggest Topics: 💡 GitHub: 💬 Discord: 💖 Membership: 🛒 Store: 🖋️ Twitter: 📸 Instagram: 🎥 Coding Challenges: 🎥 Intro to Programming: 🔗 : 🔗 Web Editor: 🔗 Processing: 📄 Code of Conduct: This description was auto-generated. If you see a problem, please open an issue: #apolloniangasket #pi #circlepacking #complexnumbers #curvature #descartestheorem #p5js #javascript =====================================================