I'm minded to tile the floor in a bathroom and a toilet with Portuguese terracotta tiles, in an aperiodic tiling (like Penrose's, but using squares and equilateral triangles; see https://tilings.math.uni-bielefeld.de/substitution/square-triangle/). Before I go further: is there a reason why I should *not* do this? The tiles are not cheap (ca. 200 eur/m^2), so this would be an expensive mistake. (Well, perhaps not compared to other expensive mistakes: the total area to be tiled is between 8 and 9m^2.)

 

https://newterracotta.com/tiles/

 

PS. I am looking for reasons such as "it won't last" or "you will slip and break your neck", not "I hate maths".

 

Here are some samples. (I also got others, but these seem to be colours that fit together. I should choose two or three.)

 

Edited October 20, 20223 yr by Garald

How do the triangles and squares fit together without large grout gaps?

4 hours ago, Temp said:

How do the triangles and squares fit together without large grout gaps?

 

Oh ye of little faith!

 

https://tilings.math.uni-bielefeld.de/substitution/square-triangle/

 

and of course also less complex ways.

11 hours ago, Garald said:

 

Yes but the square in the photo appear to have sides longer than the sides of the triangle. You would have to cut every square tile smaller. 

 

 

Edited October 20, 20223 yr by Temp

PS I do love the colour of the triangular tile.

4 minutes ago, Temp said:

 

Yes but the square in the photo appear to have sides longer than the sides of the triangle. You would have to cut every square tile smaller. 

 

 

 

Optical illusion. See:

 

At any rate, here is a segment of the pattern that I could use for my bathroom (about 280cm by 210cm, once insulation is installed). The plan is to have the pattern even on the shower floor (there is no bathtub). I forgot to take the width of the grout (2mm to 3mm) into account, so one should probably omit the last row and the last column or so.

 

Here's a larger pattern (produced by some Python code I hacked up yesterday). One can pick up whatever rectangular "windows" one wants. As an example, I've selected one window of the size of my bathroom and one that is toilet-sized (70cm by 210cm). It is also possible to produced patterns that, while still aperiodic, have more symmetry. I'm attaching an example with 12-fold symmetry.

example1clear.pdf example1veryclear.pdf example3clear.pdf

Edited October 27, 20223 yr by Garald