Roger Penrose — the English mathematical physicist who shared the 2020 Nobel Prize in Physics for the discovery that black hole formation is a robust prediction of the general theory of relativity — is also famous for something more terrestrial - Penrose Tiling. Here’s a look at the other side of the Nobel laureate:Tile High: Back in the 1970s, Roger Penrose created a set of tiles that could be used to cover an infinite plane in a pattern that never repeats. His work changed our basic understanding of design, showing how infinite variations could be created within a highly ordered environment. Patterns of Penrose
Inside the Palace - Palace of Venaria (Turin, Italy) The Palace of Venaria is a former royal residence located in Venaria Reale, near Turin, in Piedmont, northern Italy. It is one of the Residences...
A Penrose tiling (Wikipedia), named for British mathematical physicist Sir Roger Penrose, who investigated them in the 1970s. A Penrose tiling is "aperiodic," or, simply put, produces a pattern that does not repeat itself no matter how far you extend it across the plain. All Penrose tilings are aperiodic, but not all aperiodic tilings are Penrose tilings. Lots of bright creative folks have installed custom Penrose tile floors. Here's a selection of a few of my faves from around the web. I couldn't find anybody online who's selling pre-cut Penrose prototiles, so it looks like anybody who wants to do it themselves has to cut their own. Or, if somebody is feeling entrepreneurial...
If made with rhombs with 3" sides, this should work out to be right at 44" square. Image created from PDF files generated by Alan Schoen. Used with permission.
Prismatic Penrose Tiles
If made with rhombs with 3" sides, this should work out to be right at 44" square. Image created from PDF files generated by Alan Schoen. Used with permission.
I just finished another Penrose tile quilt: First - Credit where it's due... If you do a Google Image search on 'Penrose tile quilt' the top three results will be this awesome quilt: This lovely quilt was made by Serena Mylchreest nearly 20 years ago. This obviously was an inspiration for my design. The element of the Mylchreest design that I borrowed is the way the rhombi are divided in half (fat rhombi divided lengthwise, and the thin rhombi split on the narrow diagonal) so it is tiled with triangles instead of rhombi. Then the critical design element is to select colors of different values for the 'light half' and 'dark half' of the rhombi to create the nifty 3-D effect. I was pleased with the way my last Penrose tile quilt turned out when I first came up with the notion to machine piece the patches before I English paper pieced the rhombi. So I played around with some other machine piecable patterns and this was one of the results. When I designed the layout, I wanted to make a Penrose tiling that was not radially symmetrical through the center like my last quilt (and most Penrose tile quilts). I find their quasi-periodic nature one of the more mind bending elements of Penrose tilings, and I feel this is not obvious when it is radially symmetrical. I began with this simple layout: The yellow dots indicate the eventual location of the yellow stars. The black square roughly indicates the final border of the quilt. Then I deflate the rhombi 3 levels thusly: I explain inflation/deflation of Penrose tiles more thoroughly in this post. After removing the superfluous rhombi, we're left with this base layout: Then we add these machine piece rhombi: One last design decision I made was to inflate just five of the rhombi to make the one large star. Two other designs I came up with while playing with machine-pieced rhombi:
