I Used the Cantor Set Construction to Make a Short Horror Clip | Nathan Dalaklis 

🤔Quite honestly, I don't think I know enough math to answer this question completely. But, I'll at least give the first part a go.😀 To my recollection, a lot of the ideas in fractal geometry, especially ideas like Hausdorff dimension, were developed as an argument against the assumption of classical analysis that in essence "the world is smooth", a lot of devices in Calculus require some level of "smoothness" in our mathematical objects or functions in order to properly analyze them (think n-differentiability, or properties that have the 'almost everywhere' qualifier and integrability). Contrary to those ideas, dimension calculations like Hausdorff and Box dimension, and other dynamical measures like Topological entropy that come up in Symbolic Dynamics which is closely related to some areas of Fractal Geometry don't depend on this "smoothness". For example, we can do the same Box dimension analysis on a circle as we can on any resolution of the coastline of India because we don't require much in the Box Dimension calculation, but we can't necessarily integrate any given resolution of the coastline of India because as we look at finer and finer samples we'll realize it doesn't have the "smoothness" an integrable function 'should' have Of course, I'm being very hand-wavy with this one 😕, but I think my main point is that Calculus and the Analysis in Fractal Geometry are both different types of analysis and they both measure and focus on different things under different assumptions.

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Thanks! 🙂

Also to be honest i'm too weirded out to understand the educational part with regards to fractals ...

:D That's alright my goal here wasn't necessarily to go through the details in depth. This video mostly just arose from the thought that I could apply the cantor set construction to video and then I wanted to put that thought into one of my RU-vid videos. I was weirded out by the result too...