The shape of $x^2<mrow><mi\; mathvariant="normal">m</mi><mi\; mathvariant="normal">o</mi><mi\; mathvariant="normal">d</mi></mrow>n$

We examine the graphs generated by the map $x\mapsto x^{2}n$ for various $n$, present some results on the structure of these graphs, and compute some very cool examples.