To give a talk to 17-18 years old (who have a knack for mathematics) about how interesting mathematics (and more specifically pure mathematics) can be, I wanted to use nice facts accompanied by nice looking visualizations. However, the underlying mathematics should not be too trivial, otherwise it will not seem challenging to the students. I already looked into [Chaos-Math](http://www.chaos-math.org/en) and [Dimensions-Math](http://www.dimensions-math.org/Dim_E.htm), which provided me with useful material, and I was wondering if anyone knows of similar things? I'm sure there have to be things in differential geometry, or topology, that are equally inviting!

Thanks!