#penrose tiling

[andmaybegayer]

Penrose quilt is officially finished! 2022-07-30 to 2023-04-02, all hand sewn by me and my mother.

It would figure that the Einstein would be found like a month before I finished this! Honestly probably for the best, the Einstein has too many concave angles.

We'll embroider patches for it soon but for now we're calling it, it still needs its first wash and I'll probably have to patch up some quilting after that.

[threadedtheorems]

Why have a regular star when you can have a mathematical star? ✨

This star is a section of the Penrose tiling, an aperiodic tiling that can cover the plane without having a repeating pattern. In the tiling, small symmetric areas like this star appear, but they don’t join together in a uniform way.

[michaelrotonal]

tried to sketch a penrose tiling

the outline should be a regular decagon

[proteus-thrmanfish]

[high-fructose-jay-syrup]

wHAT DO YOU MEAN PENROSE TILINGS ARE NAMED AFTER ROGER PENROSE I THOUGHT IT WAS JUST BECAUSE THEY INVOLVED PENTAGONS AND LOOKED LIKE A ROSE

[paulfc]

Origami Penrose Tessellation

When Roger Penrose did the work that resulted in the now famous Penrose tiling schemes he discovered a number of things about tiling, periodic and aperiodic.  The main question he answered was “What is the minimum number of tiles to force aperiodic tiling of the plane?”  and the answer is two provided that you follow the rules as to how they are juxtaposed.  The shapes of the tiles are however not limited.  He suggested the famous Kites and Darts but he also demonstrated that a fat rhombus and a thin one with given internal angles also works.  There are curved versions and jigsaw puzzle like versions also.

Having had a little play at Origami Tessellation with Kites and Darts and finding it somewhat problematic I thought I might try his alternative.

This is my construction and colouring of his rhombs again starting with an area that demonstrates five fold symmetry, the colouring of the tiles is to force you to obey the placement rules and it incidentally often has aesthetic appeal.

In this case and somewhat anti-aesthetic, it rather reminds me of a football.

[andmaybegayer]

Quilting complete

I bought 30g of perle to do this and this is all that's left. I used one reel and my mother used two which is pretty much exactly our relative difference in sewing speed. Lean Manufacturing Dot JPEG. Next up is binding the edge.

[andmaybegayer]

Taking on the very ambitious project of a Penrose Tiling quilt, I worked out rough dimensions in Inkscape earlier so now I have that and I got fabric.

I'm doing this with my mother who has done several quilts in the past so I'm pretty sure a) I'll actually finish it and b) it will turn out pretty well.

The power cut so I didn't get a chance to do a test tiling with some scrap fabric.