What is Multifractal Analysis? Modern Fractal Geometry and my research

Hausdorff dimension is not a fine enough analysis for many objects of interest in modern fractal geometry. Luckily Hausdorff dimension can be adapted to the study of multifractals or a multifractal decomposition via multifractal analysis. This area of modern fractal geometry is core to my math phd research area for my dissertation, and so I wanted to spend a bit of time trying to communicate a bit about it here. In the process we'll connect fractal constructions and measure theory to generate a "irregular" fractal where such a multifractal analysis is required and then give an overview of what such an analysis would involve. 00:00 Intro 00:14 What is studied in fractal geometry? 03:10 A fractal with "irregularity" 07:11 Nathan's mid video math comm crisis 07:58 A multifractal analysis with respect to local dimension ______ Last PhD Update: https://youtu.be/RdB71jkjBSk Last Academic Talk/stream: https://youtu.be/--LsBI3wHmQ Last CHALK video: https://youtu.be/tIcZ6FwuWCQ The CHALKboard: http://www.youtube.com/c/CHALKboard My website: https://nathandalaklis.com Help support my videos: https://ko-fi.com/chalknd ______ WHAT GEAR I USED FOR THIS VIDEO: Camera Kit - https://amzn.to/3PrzRKB SD card - https://amzn.to/2PbTiag Lighting Kit - https://amzn.to/3ffibMH Editing Hard Drive - https://amzn.to/2P7hSsM DISCLAIMER: Links included in this description may be affiliate links. If you purchase a product or service with the links that I include here, I may receive a small commission. There is no additional charge to you! Thank you for supporting my channel and for helping me create these free videos! Subscriber Count as of last CHALK video: =====