Coding Challenge 182: Apollonian Gasket Fractal

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

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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://youtu.be/Bxdt6T_1qgc?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
🎥 All: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH

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://youtu.be/6z7GQewK-Ks
🚂 22 Julia Set in Processing: https://youtu.be/fAsaSkmbF5s
🚂 77 Recursion: https://youtu.be/jPsZwrV9ld0
🚂 50 Circle Packing: https://youtu.be/QHEQuoIKgNE
🚂 95 Approximating the Value of Pi: https://youtu.be/5cNnf_7e92Q
🚂 96 Visualizing the Digits of Pi: https://youtu.be/WEd_UIKG-uc
🚂 97 The Book of Pi: https://youtu.be/tbvG9hrJxOU
🚂 139 Calculating Digits of Pi with Collisions: https://youtu.be/PoW8g67XNxA
🚂 140 Leibniz Formula for Pi: https://youtu.be/uH4trBNn540
🚂 141 Calculating Digits of Pi with Mandelbrot Set: https://youtu.be/pn2vlselv_g
🚂 169 Pi in the Sky Game: https://youtu.be/_H9JIwWP7HQ
🚂 176 Buffon's Needle: https://youtu.be/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 arbitrary 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

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🎥 Coding Challenges: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
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🔗 p5.js: https://p5js.org
🔗 p5.js Web Editor: https://editor.p5js.org/
🔗 Processing: https://processing.org

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