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/182-apollonian-gasket 🚀 Watch this video ad-free on Nebula https://nebula.tv/videos/codingtrain-coding-challenge-182-apollonian-gasket p5.js Web Editor Sketches: 🕹️ Apollonian Gasket: https://editor.p5js.org/codingtrain/sketches/zrq8KHXnO 🕹️ Colorful Recursive Gaskets in Gaskets: https://editor.p5js.org/codingtrain/sketches/leBpmVwaM 🎥 Previous: https://www.youtube.com/watch?v=Bxdt6T_1qgc 🎥 All:    • Coding Challenges   References: 🔗 Apollonian Gasket: https://en.wikipedia.org/wiki/Apollonian_gasket 🔗 A Tisket, a Tasket, an Apollonian Gasket: https://www.americanscientist.org/article/a-tisket-a-tasket-an-apollonian-gasket 🔗 Apollonian Gaskets: https://mathlesstraveled.com/2016/04/27/apollonian-gaskets/ 🔗 Beyond the Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf 🔗 The Kiss Precise: https://www.nature.com/articles/1371021a0#preview 🔗 Frederick Soddy: https://en.wikipedia.org/wiki/Frederick_Soddy 🔗 Problem of Apollonius: https://en.wikipedia.org/wiki/Problem_of_Apollonius 🔗 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/Descartes%27_theorem 🔗 Complex.js: https://www.npmjs.com/package/complex.js Related Coding Challenges: 🚂 21 Mandelbrot Set with p5.js: https://www.youtube.com/watch?v=6z7GQewK-Ks 🚂 22 Julia Set in Processing: https://www.youtube.com/watch?v=fAsaSkmbF5s 🚂 77 Recursion: https://www.youtube.com/watch?v=jPsZwrV9ld0 🚂 50 Circle Packing: https://www.youtube.com/watch?v=QHEQuoIKgNE 🚂 95 Approximating the Value of Pi: https://www.youtube.com/watch?v=5cNnf_7e92Q 🚂 96 Visualizing the Digits of Pi: https://www.youtube.com/watch?v=WEd_UIKG-uc 🚂 97 The Book of Pi: https://www.youtube.com/watch?v=tbvG9hrJxOU 🚂 139 Calculating Digits of Pi with Collisions: https://www.youtube.com/watch?v=PoW8g67XNxA 🚂 140 Leibniz Formula for Pi: https://www.youtube.com/watch?v=uH4trBNn540 🚂 141 Calculating Digits of Pi with Mandelbrot Set: https://www.youtube.com/watch?v=pn2vlselv_g 🚂 169 Pi in the Sky Game: https://www.youtube.com/watch?v=_H9JIwWP7HQ 🚂 176 Buffon's Needle: https://www.youtube.com/watch?v=h5ZNcAPXxew 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/ 👾 Share Your Creation! https://thecodingtrain.com/guides/passenger-showcase-guide 🚩 Suggest Topics: https://github.com/CodingTrain/Suggestion-Box 💡 GitHub: https://github.com/CodingTrain 💬 Discord: https://thecodingtrain.com/discord 💖 Membership: null 🛒 Store: https://standard.tv/codingtrain 🖋️ Twitter: https://twitter.com/thecodingtrain 📸 Instagram: https://www.instagram.com/the.coding.train/ 🎥 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-of-Conduct This description was auto-generated. If you see a problem, please open an issue: https://github.com/CodingTrain/thecodingtrain.com/issues/new #apolloniangasket #pi #circlepacking #complexnumbers #curvature #descartestheorem #p5js #javascript =====================================================