Penrose tiling is an aperiodic tiling. A tiling is a covering of the plane by non-overlapping polygons or other shapes, and aperiodic means that shifting any tiling by any finite distance cannot produce the same tiling.
A moiré pattern is a large-scale interference pattern that can be produced when a pattern is overlaid on another similar pattern.
For more information watch these videos:
On this page you can see two 4000x4000 image with Penrose tiling on top of each other.
Use your browser to move around and zoom out to see the whole picture.
To create the moiré pattern use your keyboard to move one of the layers: