Einstein Tile Part 2: Exploring tiling techniques using Inkscape (Hat Tile / Aperiodic Monotile)
SVG File for Einstein Tile / Arrow: https://mistercorzi.scot/svg/hat-arro...
This video explains a tiling method for the Einstein tile known as the Hat. It uses four Supertiles (Hexagon, Triangle, Parallelogram, Fan or pentagonal Fylfot blade) to create a tiling of supertiles. The underlying Hats force matching constraints on the supertiles. Orientation arrows are used to help guide the correct extension of the tiling.
The Einstein Tile called the Hat was discovered by David Smith (UK) and further researched by Joseph Samuel Myers (UK), Craig S. Kaplan (Canada) and Chaim Goodman-Strauss (US). The preprint paper announcing their discovery and detailing their proof of aperiodic tiling (and non-periodic tiling) was published on the ArXiv site on 20th March 2023. Here is the link to the paper: https://arxiv.org/abs/2303.10798
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Chapters
0:00 Introduction
0:43 Document preparation / Import tile
2:43 Hexagon Supertile construction
5:36 Triangle Supertile construction
6:49 Parallelogram Supertile construction
8:20 Fan Supertile construction
10:44 Placing the Arrow Guides
13:09 Supertiling: the 1st iteration
16:45 Supertiling: the 2nd iteration
19:20 Hints of larger structures
20:13 End links
Other videos in this series are:
Using Inkscape to construct the Penrose Tiles (Part 1: Outline shape of the Kite and Dart) • Using Inkscape to construct the Penrose Ti...
Using Inkscape to construct the Penrose Tiles (Part 2: Constructing the edge constraint patterns) • Using Inkscape to construct the Penrose Ti...
Using Inkscape to construct the Penrose Tiles (Part 3: Exploring Penrose Tiling (Kites and Darts)) • Using Inkscape to construct the Penrose Ti...
Using Inkscape to construct the Penrose Tiles (Part 4: Inflating a Penrose Tiling (Kites and Darts)) • Using Inkscape to construct the Penrose Ti...
Penrose Tiles Part 5 - Kites, Darts, Inflation, Fibonacci Numbers and the Golden Ratio • Penrose Tiles Part 5 - Kites, Darts, Infla...
Beyond the Penrose Tiles Part 6 - Einstein Tile: How to Construct an Aperiodic Monotile Using Inkscape (The Hat Tile) • Einstein Tile - How to Construct an Aperio...