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How (and why) to take a logarithm of an image How (and why) to take a logarithm of an image 45 min Her Eyes Were Green Her Eyes Were Green 7 min 13 most EXPENSIVE Tech Fails of all time 13 most EXPENSIVE Tech Fails of all time 24 min This 1950's ATV Concept ? This 1950's ATV Concept ? 15 min I Investigated IKEA’s Suspiciously Cheap Tech I Investigated IKEA’s Suspiciously Cheap Tech 18 min Игра Без Сохранений (Мото VLOG) Игра Без Сохранений (Мото VLOG) 44 min A COLD Knife is ok BUT this…. A COLD Knife is ok BUT this…. 17 min The Most Interesting Displays In The World! The Most Interesting Displays In The World! 16 min Sawing a Dam in Half (on Purpose) Sawing a Dam in Half (on Purpose) 21 min Я загрузил ИИ в Скайрим... и теперь городом правит пёс 👑 Я загрузил ИИ в Скайрим... и теперь городом правит пёс 👑 25 min Игра Без Сохранений 2 (Мото VLOG) Игра Без Сохранений 2 (Мото VLOG) 58 min The Insane Engineering of the P-38 Lightning The Insane Engineering of the P-38 Lightning 27 min How Will the Golden Dome Work? How Will the Golden Dome Work? 23 min Do cranberries help prevent UTIs? #shorts #science #stem #scishow Do cranberries help prevent UTIs? #shorts #science #stem #scishow 1 min How to explain something complicated How to explain something complicated 10 min Why do some British trains still rely on old levers? Why do some British trains still rely on old levers? 26 min How We Built the ISS - Part 2 How We Built the ISS - Part 2 29 min Sony Just Brought Super Zoom Cameras Back From the Dead! (RX10V) Sony Just Brought Super Zoom Cameras Back From the Dead! (RX10V) 1 min Abandoned - Nara Dreamland Abandoned - Nara Dreamland 17 min How Do We Write Backwards?! 🤯 How Do We Write Backwards?! 🤯 1 min What is sumo, and why is it so popular? - Lee Thompson What is sumo, and why is it so popular? - Lee Thompson 6 min Why You Should Get Your DNA Sequenced After You Die Why You Should Get Your DNA Sequenced After You Die 10 min The Hidden Engineering of Runways The Hidden Engineering of Runways 19 min This substance could revolutionize human waste This substance could revolutionize human waste 10 min If you found candy with my name in it, here's why. If you found candy with my name in it, here's why. 18 min How Firefly is Revolutionizing the Logistics of Spaceflight | Full Documentary How Firefly is Revolutionizing the Logistics of Spaceflight | Full Documentary 49 min Why It's So Hard to Make Artificial Cork Why It's So Hard to Make Artificial Cork 9 min The Unlikely Rise of the Indian Space Program The Unlikely Rise of the Indian Space Program 29 min The Kurzgesagt Situation is Insane The Kurzgesagt Situation is Insane 12 min How Do Minerals Form?: Crash Course Geology #5 How Do Minerals Form?: Crash Course Geology #5 10 min This single-celled organism is HUGE. #shorts #science #SciShow This single-celled organism is HUGE. #shorts #science #SciShow 1 min The Insane Engineering of Europa Clipper The Insane Engineering of Europa Clipper 21 min The deadly drug everyone is taking The deadly drug everyone is taking 10 min Why do male nipples exist? Why do male nipples exist? 1 min So hot underground it smokes!! So hot underground it smokes!! 1 min I put high Speed Prop Blades on my Kayak Paddle!! I put high Speed Prop Blades on my Kayak Paddle!! 15 min Why do gay people sound like that? Why do gay people sound like that? 6 min Name That Infrastructure (Ep. 2) #shorts Name That Infrastructure (Ep. 2) #shorts 1 min Are birds getting smaller? #shorts #science #scishow #climatechange Are birds getting smaller? #shorts #science #scishow #climatechange 1 min Who else could use these? ​⁠@nike #teamnike #ad Who else could use these? ​⁠@nike #teamnike #ad 1 min The Dark Side of the World’s Lightest Structural Metal The Dark Side of the World’s Lightest Structural Metal 16 min The Forbidden Alloy of WW2 The Forbidden Alloy of WW2 2 min What do you think? What do you think? 2 min How We Built The ISS How We Built The ISS 37 min Is the Secret to Treating Schizophrenia in... Engineering? Is the Secret to Treating Schizophrenia in... Engineering? 23 min This is NUTS This is NUTS 1 min SciShow is heading into the field TOMORROW with the all new Field Trips mini series. SciShow is heading into the field TOMORROW with the all new Field Trips mini series. 1 min Choose your Whip Choose your Whip 2 min Drilling Into Rock With Radiation Drilling Into Rock With Radiation 2 min The Insane Engineering of the F-14 Tomcat The Insane Engineering of the F-14 Tomcat 30 min Why Everything Weighs Less in Antarctica Why Everything Weighs Less in Antarctica 12 min

How (and why) to take a logarithm of an image

2026 45 min

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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