6 papers
A7: An aperiodic set of 7 square dominoes
Vincent Van Dongen
This paper presents an aperiodic tileset of 7 square dominoes. We call it A7 as it directly relates to the aperiodic set Ammann A3. We start with a description of the tileset. We t…
Ax, 3 polyominoes for tiling the plane non-periodically
Vincent Van Dongen, Pierre Gradit
How do people come up with new sets of tiles including new tile shapes that would only tile non-periodically? This paper presents our graphical journey in tilings and provides a ne…
An aperiodic monotile for the tiler
Vincent Van Dongen
Can the entire plane be paved with a single tile that forces aperiodicity? This is known as the ein Stein problem (in German, ein Stein means one tile). This paper presents an aper…
A self-ruling monotile for aperiodic tiling
Pierre Gradit, Vincent Van Dongen
Can the entire plane be paved with a single tile that forces aperiodicity? This is known as the ein Stein problem (in German, ein Stein means one tile). This paper presents a monot…
An aperiodic tiling made of one tile, a triangle
Vincent Van Dongen
How many different tiles are needed at the minimum to create aperiodicity? Several tilings made of two tiles were discovered, the first one being by Penrose in the seventies. Since…
An aperiodic tiling of variable geometry made of two tiles, a triangle and a rhombus of any angle
Vincent Van Dongen
Aperiodic tiling is a well-know area of research. First developed by mathematicians for the mathematical challenge they represent and the beauty of their resulting patterns, they b…