The Fascinating Math behind Piston Extenders #SoME3

This is my submission for the Summer of Math Exposition, hosted by @3blue1brown https://some.3b1b.co/ Patreon: https://www.patreon.com/mattbatwings Discord: https://discord.gg/V5KFaF63mV My socials: https://linktr.ee/mattbatwings My texture pack: https://modrinth.com/resourcepack/mattpack World Download: (JAVA 1.18.2) https://www.planetminecraft.com/project/infinite-piston-extender/ Piston Animations created by @Sloimay 0:00 Introduction 0:36 What is Minecraft? 1:42 What is a Piston Extender? 2:16 Problem Statement 2:35 Extension Sequences 8:51 Extension Optimality 9:13 Extension Parallelization 11:11 Extension Circuit 12:38 Retraction Sequences 16:15 Retraction Optimality 17:16 Retraction Parallelization 17:40 Retraction Circuit 18:52 Showcase 19:45 Thanks for watching! Music (in order): Patricia Taxxon - Wavetable https://youtu.be/p9zuIoJ-y3M LAKEY INSPIRED - Chill Day https://youtu.be/3HjG1Y4QpVA Infraction - Serotonin https://youtu.be/saNSLwgRkrw Harris Heller - Streamline https://youtu.be/GB7SYPFs7QQ Harris Heller - Plethora https://youtu.be/4U3iFdSyNuI Harris Heller - Tokyo Rain https://youtu.be/WtOcNctiLfY Harris Heller - Iridescent https://youtu.be/FWXzp8THOuc Harris Heller - Path Less Traveled https://youtu.be/l_o56ny2aao Harris Heller - In My Shadow https://youtu.be/Y2dk4PnO5lA Harris Heller - 90's https://youtu.be/1Ct-kEcajJQ Sascha Ende - Finger ins Ohr https://youtu.be/8jFDyrzU1Ag JNATHYN - Dioma https://youtu.be/r2Ig85ycGKQ Gucci Louis - Rap Beat 2 https://youtu.be/v7tiSGnGRlk Mokka - Only You and Me https://youtu.be/a08OsBSt4cM Harris Heller - Manhattan Project https://youtu.be/s02K_ofVPJc Harris Heller - Golden Age https://youtu.be/Ws205UM0GzM Harris Heller - Guilty Spark https://youtu.be/w9M1_ZoxP54 Alexander Nakarada - Favorite https://youtu.be/eDdEsfMBtFQ Infraction - Sapporo https://youtu.be/l-QRgBonhCo JNATHYN - Dioma https://youtu.be/r2Ig85ycGKQ Gee - Electroswing Revival https://youtu.be/ZkkNgbkcvog Jeremy Blake - Heaven and Hell https://youtu.be/IL5AhzUSVR4 mellowind - Bored || Vibin in the 80s https://youtu.be/LjwftaQchP4