Using Inkscape to construct the Penrose Tiles (Part 4: Inflating a Penrose Tiling (Kites and Darts))

https://mistercorzi.scot/svg/penrose.svg Right click –› save to computer –› open in Inkscape if you wish to try the activities in the video.
https://mistercorzi.scot/pdf/cut-out.pdf Print on card and cut out to create a set of Penrose tiles. Attempting to create a Penrose tiling is the best way to become familiar with the Dart and the Kite tiles.
In this 4th video the process of inflation is explained. The process is demonstrated using the Kite as the starting tile and is taken to two iterations.
The previous three videos gave step by step instructions on how to use the free Open Source Inkscape software to geometrically construct the Penrose Tiles and explore some basic configurations.
The Penrose Tiles were discovered by Roger Penrose in 1974. The two tiles used in these videos were named by John Conway "Kite" and "Dart". They can tile the plane but only in a non-periodic way and are called Aperiodic Tiles for this reason.
If you attempt a tiling with the Penrose Tiles as you build a larger and larger region you soon find places where no tile will fit. You will need to unpick some of your tiling before you can proceed further.
It has been said of these tilings:
"most patterns, like the universe, are a mystifying mixture of order and unexpected deviations from order. As the patterns end, they seem to be always striving to repeat themselves but never quite managing it".