When you take two copies of the Penrose tiling, as Penrose himself demonstrated, they form a 5 fold symmetric Moire pattern which matches the 5 fold symmetry of their construction. When you "zoom into" one of the bright spots, being a region where the two tilings agree more and hence block less light, we find a placement of the two tilings which agrees almost everywhere between them, and the odd surprise was that where they disagree is consolidated into linear features which defined whole regions of agreement. 
When this is done with the newly discovered (June 2023) Spectre tile, which is chiral, we see the same sort of behavior forming a 6 fold symmetric Moire pattern, but the disagreements are no longer perfectly linear. Here is a large picture of such a near-perfect overlay:
If we zoom into one of these junctions of wiggles we can see that there are two kinds, one that zig-zags, and one that zig-flat-zag-flats:
This is odd to me, and if we look at the 8 wiggles coming into and out of the nexus, we find they are matched up 4 and 4 of the two kinds of wiggles. We note that it appears the angle made between the light red and yellow is the same as the angle between the orange and the dark red implying perhaps we should consider these to be deflections of the same wiggle through the nexus. Likewise the angle between grey and blue is the same as between green and purple implying the same.
The last thing I want to put out there is that if change the angle as far from perfectly overlapped as you can, then you will still find many tiles which still match up while the rest get cut up into various tiles and meta-tiles from the wheel tiling and beyond and it is some of these shapes which make up the vertebrae of the wiggles:
My question is very generally, why is this? why two kinds of quasi-linear disagreements while Penrose only has the one? Why deflect through intersections? is this also happening for Penrose but simply deflecting by 1/5 a turn to seemingly land on the other lines but actually doing similar? What possible region shapes are there? how many times can two wiggles intersect? etc.
Edit: just made a new and fairly profound observation about these wiggle patterns, they appear to naturally generate with 2-fold symmetry. Below are 3 images which i have tried to boost for viewing which feature simple-to-complex wiggle networks that appear to maintain 180 degree rotational symmetry:
Which comes along with a whole host of other natural questions I'm sure the reader can think of themselves.