Just for fun, here’s a thread of tilings from https://tilings.math.uni-bielefeld.de/ that I particularly like.
Tilings Encyclopedia | Tilings Encyclopedia

Robinson Triangle. A variant of Penrose tiling made of two shapes of triangle. Lovely!

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

Tilings Encyclopedia | Robinson Triangle

Chord Quadrangle 3-3

I probably like this one mainly because it uses the same shape I’ve been playing with, but the way it’s constructed is pretty nice.

https://tilings.math.uni-bielefeld.de/substitution/chord-quadrangle-3-3/

Tilings Encyclopedia | Chord Quadrangle 3-3

Equithirds

I mean, just look at it. It’s beautiful!

https://tilings.math.uni-bielefeld.de/substitution/equithirds/

Tilings Encyclopedia | Equithirds

Overlapping Robinson Triangle I

This is cool because it breaks one of the primary rules of tilings: that tiles are not allowed to overlap.

https://tilings.math.uni-bielefeld.de/substitution/overlapping-robinson-triangle-1/

Tilings Encyclopedia | Overlapping Robinson Triangle I

Plate Tiling

There’s no information about this one at all. Just a picture. Very mysterious!

https://tilings.math.uni-bielefeld.de/substitution/plate-tiling/

Tilings Encyclopedia | Plate Tiling

Psychedelic Penrose variant I

One of several “psychedelic” variants of the Robinson Triangles, this one is my favourite.

https://tilings.math.uni-bielefeld.de/substitution/psychedelic-penrose-variant-1/

Tilings Encyclopedia | Psychedelic Penrose variant I

Rorschach

This is fun because it looks *so* periodic, even though it’s not.

https://tilings.math.uni-bielefeld.de/substitution/rorschach/

Tilings Encyclopedia | Rorschach

Square-triangle

Just a square and an equilateral triangle. It doesn’t get much simpler than that.

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

Tilings Encyclopedia | Square-triangle

Trihex

It just looks so sinister and mysterious.

https://tilings.math.uni-bielefeld.de/substitution/trihex/

Tilings Encyclopedia | Trihex

Tuebingen Triangle

A particularly nice example of the delicious balance between order and chaos that non-periodic tilings display so beautifully.

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

Tilings Encyclopedia | Tuebingen Triangle