I am preparing a report for student conference on the mathematics. The main objective of a report is to overview history of fractals, both from theoretical and applied viewpoint. The only problem is that my current version, as I see it, doesn’t contain enough examples of actual problems related to fractals.

So, the question is: what are examples of such problems which are available to understand for average math student? (studied Calculus I and II, Linear Algebra, Differential Equations and some functional analysis)