Question: Modifying plot geometry

I was playing with some of the geometry plotting in maple for fun(I rarely use it) and came up with an IFS like system. While I'm sure maple sucks for IFS it is somewhat easy to do. I was just using rectangles though.

Is there any way though to modify a shape using a transform such as a complex map? Not just the vertices but the edges too.

Also, is there any way to do a complex map in some easy way? e.g., "paint the geometry on to a texture" and then map it with a complex plot. Usually one just uses a pixel coloring map and maps that, which would be fine for playing around but I'd like to have more control.

Basically draw something on a plot(geometry, functions, image, etc), transform them in some interesting way(e.g., complex map) and then IFS them to get interesting visuals.

I realize one can do this in maple by turning the edges in to curves and all that mess but I'd like to avoid that since maple is not really good at it anyways(would probably end up very slow).