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How (and why) to take a logarithm of an image 45 分钟 
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2026 45 分钟
Escher's Print Gallery, and the tour of complex analysis it invites. Explore our virtual career fair: https://3b1b.co/talent Join channel supporters to see videos early: https://3b1b.co/support An equally valuable form of support is to share the videos. Home page: https://www.3blue1brown.com Original paper by de Smit and Lenstra: https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-lenstra-escher.pdf The book I was showing is "Magic of MC Escher" by J. L. Locher https://amzn.to/4d7zXTT If you want to play with this concept interactively, Jürgen Richter-Gebert put together a nice page: https://mathvisuals.org/PrintGallery/ This piece was co-written by Paul Dancstep, who handled many of the animations in the art section, including the delightful mesh warp scene. Aaron Gostein helped with the manim animations in the section introducing complex functions. Artwork provided by Talia Gershon, Mitchell Zemil, and Anna Fedczuk. https://sites.google.com/view/taliagershon https://mitchellzemil.com/ https://anna-fedczuk.framer.website/about Music by Vincent Rubinetti Timestamps: 0:00 - The print gallery 13:04 - Conformal maps from complex analysis 21:41 - The complex exponential 25:56 - The complex logarithm 32:32 - 3b1b Talent 33:14 - Constructing the key function 40:16 - The deeper math behind Escher Correction: at 18:10, the function graph does not match the function definition that appears in the top right corner: f(x) = x^3 + 3x^2 - x - 4. Instead of -4, there should be -3: f(x) = x^3 + 3x^2 - x - 3. ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://3b1b.co/faq#manim ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: https://3blue1brown.substack.com Twitter: https://twitter.com/3blue1brown Bluesky: https://bsky.app/profile/3blue1brown.com Instagram: https://www.instagram.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Facebook: https://www.facebook.com/3blue1brown Patreon: https://patreon.com/3blue1brown Website: https://www.3blue1brown.com
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