Here is a Youtube video on the complex version of basic geometric shapes. It's entertaining, enlightening, and beautiful.
Here is one of the final images from the video. It's source is a simple function. But if you look at it, you'll realize it is a graphical representation of spinors. Spinors are a quantum effect that requires 720 degrees of rotation to return to their starting condition. They're supposed to be really weird and without precedent in the "Real" world. Right. They're simple functions in the complex (4-D) plane.