The following excerpt comes from the Wikipedia article on fundamental domains:
"Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain is a subset of the space which contains exactly one point from each of these orbits."
My question mostly stems from a lack of understanding of the definition, but here it is:
Q: Does a self-similar fractal tile form a fundamental domain in $\mathbb{R}^2$?
For example, the famous dragon curve (https://en.wikipedia.org/wiki/Dragon_curve) can be used to form the boundary of a fractal that can tile the plane $\mathbb{R}^2$. Specifically, I am interested in the tile found in this article; see page 84 for the picture. https://www.math.uwaterloo.ca/~wgilbert/Research/MathIntel.pdf
To state the question simply, are these tiles fundamental domains?