Penrose Tiles

We had a brief for an outside company to design candle holders that would be 3D laser engraved (you know, like those bricks of crystal with the eiffel tower floating inside, like that, but less tacky) so mine is a taper holder based on Penrose tile shapes and connection patterns.

I've developed an infatuation with Penrose Tiling. It's a tiling pattern that is aperiodic, which means that there is no translational symmetry. I find the resulting pattern, which is regular, but without repetition, very beautiful. While rhombus shapes tile periodically, they can be made aperiodic by using specific angles and joining rules. That means that in the rhombus based version of Penrose tiling (there are two others) the tiles are not only a particular shape, but can only be joined in particular ways.

I decided to show the connection rules with trees, each side of each tile has half a tree trunk, some the bottom half, some the top half, so to gather a bunch of the tiles together and build a forest through making the trees complete, you may end up with a pattern that has rotational or reflection symmetry, but it will never be translational symmetry, creating a stylised grove that still reflects some of the chaos of a real forest.

I'm bad at Rhino, and had some serious problems, but I'm learning, so that's a good thing. The nice thing about Rhino is that they've named it after something with horns on its face, so when it beats me, I don't feel stupid. I've just realised that I've got to be stubborn, like the name for a group of the program's namesake, "a stubbornness of rhinos." So... it does what it says on the tin, no?