This is very interesting! Have you done this type of analysis for other dimensions? Immediately come to mind the generalised Hausdorff dimension (defined with gauge functions), box, Assouad, etc
Cool video! I've been thinking of making a video explaining my research too. Do you have any advice about this? In particular, who is your target audience (what background knowledge are you happy to assume?) and what do you do about stuff that seems too technical to be covered well? I find myself in a particularly abstract, categorical corner of representation theory and, to be honest, I don't even know how I'm supposed to motivate what I'm doing to someone who doesn't already at least buy into representation theory as a worthwhile thing to study
I think that it is normal to want to talk about some of the technical results/ideas that you are interested in, but I usually assume that no one knows anything about what I do when I give a talk (by consequence of being the only dynamics PhD student in my department this is sometimes necessary unless I am presenting to my advisor.) Talks are not proofs (usually) so it is okay to leave some of the technical points out as long as you can address them appropriately when asked, or even talk about them at length after the talk is over. This response is to be continued, I have more thoughts, but have to run to a research meeting!
