Happy Pi Day 2024! In this video, I effort to create an Apollonian Gasket utilizing nan Descartes Circle Theorem and analyzable numbers. So galore circles! Code: https://thecodingtrain.com/challenges/182-apollonian-gasket ๐ Watch this video ad-free connected Nebula https://nebula.tv/videos/codingtrain-coding-challenge-182-apollonian-gasket p5.js Web Editor Sketches: ๐น๏ธ Apollonian Gasket: https://editor.p5js.org/codingtrain/sketches/zrq8KHXnO ๐น๏ธ Colorful Recursive Gaskets successful Gaskets: https://editor.p5js.org/codingtrain/sketches/leBpmVwaM ๐ฅ Previous: https://youtu.be/Bxdt6T_1qgc?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH ๐ฅ All: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH References: ๐ Apollonian Gasket: https://en.wikipedia.org/wiki/Apollonian_gasket ๐ A Tisket, a Tasket, an Apollonian Gasket: https://www.americanscientist.org/article/a-tisket-a-tasket-an-apollonian-gasket ๐ Apollonian Gaskets: https://mathlesstraveled.com/2016/04/27/apollonian-gaskets/ ๐ Beyond nan Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf ๐ The Kiss Precise: https://www.nature.com/articles/1371021a0#preview ๐ Frederick Soddy: https://en.wikipedia.org/wiki/Frederick_Soddy ๐ Problem of Apollonius: https://en.wikipedia.org/wiki/Problem_of_Apollonius ๐ Four Proofs of a Generalization of nan Descartes Circle Theorem: https://www.jstor.org/stable/2316373 ๐ Beyond nan Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf ๐ Descartes' theorem: https://en.wikipedia.org/wiki/Descartes%27_theorem ๐ Complex.js: https://www.npmjs.com/package/complex.js Related Coding Challenges: ๐ 21 Mandelbrot Set pinch p5.js: https://youtu.be/6z7GQewK-Ks ๐ 22 Julia Set successful Processing: https://youtu.be/fAsaSkmbF5s ๐ 77 Recursion: https://youtu.be/jPsZwrV9ld0 ๐ 50 Circle Packing: https://youtu.be/QHEQuoIKgNE ๐ 95 Approximating nan Value of Pi: https://youtu.be/5cNnf_7e92Q ๐ 96 Visualizing nan Digits of Pi: https://youtu.be/WEd_UIKG-uc ๐ 97 The Book of Pi: https://youtu.be/tbvG9hrJxOU ๐ 139 Calculating Digits of Pi pinch Collisions: https://youtu.be/PoW8g67XNxA ๐ 140 Leibniz Formula for Pi: https://youtu.be/uH4trBNn540 ๐ 141 Calculating Digits of Pi pinch Mandelbrot Set: https://youtu.be/pn2vlselv_g ๐ 169 Pi successful nan Sky Game: https://youtu.be/_H9JIwWP7HQ ๐ 176 Buffon's Needle: https://youtu.be/h5ZNcAPXxew Timestamps: 0:00 Happy PI Day!! 1:40 References 3:22 Describe nan Apollonian problem 5:51 Curvature 10:08 Start coding! 11:53 Write a usability to find nan 4th curvature 15:31 Complex numbers 21:11 Create a analyzable number class 22:52 Square guidelines of -1 25:32 Square guidelines of a analyzable number 27:57 Implement analyzable Descartes theorem 33:50 Make nan circles successful nan complexDescartes function 36:26 Use an array to adhd recursion 41:04 Validate nan circles 42:35 Check if each 4 circles are tangent 48:04 Stop adding circles erstwhile radius falls beneath a threshold 49:20 Implement arbirtary statement of circles 53:14 Debug 55:32 Possible variations 56:34 Outro Editing by Mathieu Blanchette Animations by Jason Heglund Music from Epidemic Sound ๐ Website: https://thecodingtrain.com/ ๐พ Share Your Creation! https://thecodingtrain.com/guides/passenger-showcase-guide ๐ฉ Suggest Topics: https://github.com/CodingTrain/Suggestion-Box ๐ก GitHub: https://github.com/CodingTrain ๐ฌ Discord: https://thecodingtrain.com/discord ๐ Membership: http://youtube.com/thecodingtrain/join ๐ Store: https://standard.tv/codingtrain ๐๏ธ Twitter: https://twitter.com/thecodingtrain ๐ธ Instagram: https://www.instagram.com/the.coding.train/ ๐ฅ Coding Challenges: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH ๐ฅ Intro to Programming: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6Zy51Q-x9tMWIv9cueOFTFA ๐ p5.js: https://p5js.org ๐ p5.js Web Editor: https://editor.p5js.org/ ๐ Processing: https://processing.org ๐ Code of Conduct: https://github.com/CodingTrain/Code-of-Conduct This explanation was auto-generated. If you spot a problem, please unfastened an issue: https://github.com/CodingTrain/thecodingtrain.com/issues/new #apolloniangasket #pi #circlepacking #complexnumbers #curvature #descartestheorem #p5js #javascript =====================================================
Coding Challenge 182: Apollonian Gasket
Happy Pi Day 2024! In this video, I effort to create an Apollonian Gasket utilizing nan Descartes Circle Theorem and analyzable numbers. So galore circles! Code: https://thecodingtrain.com/challenges/182-apollonian-gasket ๐ Watch this video ad-free connected Nebula https://nebula.tv/videos/codingtrain-coding-challenge-182-apollonian-gasket p5.js Web Editor Sketches: ๐น๏ธ Apollonian Gasket: https://editor.p5js.org/codingtrain/sketches/zrq8KHXnO ๐น๏ธ Colorful Recursive Gaskets successful Gaskets: https://editor.p5js.org/codingtrain/sketches/leBpmVwaM ๐ฅ Previous: https://youtu.be/Bxdt6T_1qgc?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH ๐ฅ All: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH References: ๐ Apollonian Gasket: https://en.wikipedia.org/wiki/Apollonian_gasket ๐ A Tisket, a Tasket, an Apollonian Gasket: https://www.americanscientist.org/article/a-tisket-a-tasket-an-apollonian-gasket ๐ Apollonian Gaskets: https://mathlesstraveled.com/2016/04/27/apollonian-gaskets/ ๐ Beyond nan Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf ๐ The Kiss Precise: https://www.nature.com/articles/1371021a0#preview ๐ Frederick Soddy: https://en.wikipedia.org/wiki/Frederick_Soddy ๐ Problem of Apollonius: https://en.wikipedia.org/wiki/Problem_of_Apollonius ๐ Four Proofs of a Generalization of nan Descartes Circle Theorem: https://www.jstor.org/stable/2316373 ๐ Beyond nan Descartes Circle Theorem: https://arxiv.org/pdf/math/0101066.pdf ๐ Descartes' theorem: https://en.wikipedia.org/wiki/Descartes%27_theorem ๐ Complex.js: https://www.npmjs.com/package/complex.js Related Coding Challenges: ๐ 21 Mandelbrot Set pinch p5.js: https://youtu.be/6z7GQewK-Ks ๐ 22 Julia Set successful Processing: https://youtu.be/fAsaSkmbF5s ๐ 77 Recursion: https://youtu.be/jPsZwrV9ld0 ๐ 50 Circle Packing: https://youtu.be/QHEQuoIKgNE ๐ 95 Approximating nan Value of Pi: https://youtu.be/5cNnf_7e92Q ๐ 96 Visualizing nan Digits of Pi: https://youtu.be/WEd_UIKG-uc ๐ 97 The Book of Pi: https://youtu.be/tbvG9hrJxOU ๐ 139 Calculating Digits of Pi pinch Collisions: https://youtu.be/PoW8g67XNxA ๐ 140 Leibniz Formula for Pi: https://youtu.be/uH4trBNn540 ๐ 141 Calculating Digits of Pi pinch Mandelbrot Set: https://youtu.be/pn2vlselv_g ๐ 169 Pi successful nan Sky Game: https://youtu.be/_H9JIwWP7HQ ๐ 176 Buffon's Needle: https://youtu.be/h5ZNcAPXxew Timestamps: 0:00 Happy PI Day!! 1:40 References 3:22 Describe nan Apollonian problem 5:51 Curvature 10:08 Start coding! 11:53 Write a usability to find nan 4th curvature 15:31 Complex numbers 21:11 Create a analyzable number class 22:52 Square guidelines of -1 25:32 Square guidelines of a analyzable number 27:57 Implement analyzable Descartes theorem 33:50 Make nan circles successful nan complexDescartes function 36:26 Use an array to adhd recursion 41:04 Validate nan circles 42:35 Check if each 4 circles are tangent 48:04 Stop adding circles erstwhile radius falls beneath a threshold 49:20 Implement arbirtary statement of circles 53:14 Debug 55:32 Possible variations 56:34 Outro Editing by Mathieu Blanchette Animations by Jason Heglund Music from Epidemic Sound ๐ Website: https://thecodingtrain.com/ ๐พ Share Your Creation! https://thecodingtrain.com/guides/passenger-showcase-guide ๐ฉ Suggest Topics: https://github.com/CodingTrain/Suggestion-Box ๐ก GitHub: https://github.com/CodingTrain ๐ฌ Discord: https://thecodingtrain.com/discord ๐ Membership: http://youtube.com/thecodingtrain/join ๐ Store: https://standard.tv/codingtrain ๐๏ธ Twitter: https://twitter.com/thecodingtrain ๐ธ Instagram: https://www.instagram.com/the.coding.train/ ๐ฅ Coding Challenges: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH ๐ฅ Intro to Programming: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6Zy51Q-x9tMWIv9cueOFTFA ๐ p5.js: https://p5js.org ๐ p5.js Web Editor: https://editor.p5js.org/ ๐ Processing: https://processing.org ๐ Code of Conduct: https://github.com/CodingTrain/Code-of-Conduct This explanation was auto-generated. If you spot a problem, please unfastened an issue: https://github.com/CodingTrain/thecodingtrain.com/issues/new #apolloniangasket #pi #circlepacking #complexnumbers #curvature #descartestheorem #p5js #javascript =====================================================