If a set tiles the plane, then its dimension must be two so it's not fractal. Its boundary might be fractal, though! This collection contains some notebooks that use iterated function systems to explore the possibilities.

A collection of tools and examples that make it relatively easy to generate 3D plots.
(The Right Hand Rule image taken from Wikimedia Commons under CC: https://commons.wikimedia.org/wiki/File:Right_hand_cross_product.png)