Content deleted Content added
restore images to correct paragraphs |
→Enumeration and aperiodicity: tighter |
||
Line 27:
==Enumeration and aperiodicity==
[[File:Binary-tiling-asymmetry.svg|thumb|No symmetry of the binary tiling takes the blue tile (in a middle position relative to the yellow tile two levels higher) to the red tile (in an outer position
In the square tiling of the Euclidean plane, every two tiles are positioned in the same way: there is a symmetry of the whole tiling (a [[translation (geometry)|translation]]) that takes one tile to the other. But a binary tiling does not have symmetries that take every tile to every other tile. For instance, for the four tiles two levels below any given tile, no symmetry takes a middle tile to an outer tile. Further, there is only one way of tiling the Euclidean plane by square tiles that meet edge-to-edge, but there are uncountably many edge-to-edge binary tilings.{{r|df}} The prototile of the binary tiling can be modified to force the tiling to be edge-to-edge, by adding small protrusions to some sides and matching indentations to others.{{r|radin}}
| |||