Pattern Puzzle: Escher + CAD = fun for all

Making the rounds on the intertubes of late (HT) are laser cut wooden floor tiles inspired by Escher (right).  You can buy these on Etsy.  I was sorely tempted to buy them for a future kitchen flooring project but for two things. The tiles are only 1/8″ thick and they are wooden -I wanted ceramic tile.

So after gazing longingly at them for a time, I wondered if I could make my own ceramic tiles. I don’t know if I can; I got a bit side tracked with the first part, that of making a pattern for the tile from which molds could be made.  The cheater quick step to making molds would be to buy some of the wooden tiles but that struck me as dishonest (the wooden tile producer created their own pattern) and besides, it’d take all the fun out of making the pattern myself.

Which brings us to fun ways to use CAD pattern making programs to make patterns for non-apparel or sewn product items. I still haven’t finished my project but thought I’d show you what I’ve done so far in StyleCAD and how I did it. As always, your mileage may vary.

First step was to find an image of Escher’s tessellated butterfly pattern (scroll down).

Second was to enlarge the image and print it out. I enlarged mine to about 8″ across the wing tips. While too large for floor tiles, I wanted something large enough to digitize with sufficient detail.

Third, I traced the outline of the image on the back side of the sheet and digitized it. Here is a pdf of the resulting pattern (I can post a dxf/gerber/stylecad file upon request).

Fourth…is a period of exploration which is where I’m at now. I’m discovering how the pattern interlocks (above right) so I can repair the pattern because it is not perfect. The math whizi in our midst would probably make short work of this and be able to articulate its features readily. To whit, Mr. Fashion-Incubator peered over my shoulder and said “oh, it’s a hexagon”.

My brain works with patterns in ways I can’t articulate, not having the context that a solid grounding in math provides. The first thing I saw was a circle (lower right). A series of them actually. My CAD program makes instant work of circle drafting and one can similarly quickly, assign however many divisions (points) one would want to the circle. I created a segmented circle pattern if you want to play with it yourself.

I took careful notes as to the circle sizes and the relationship to the butterfly shapes within them -and that’s where it is for now.

Currently, the figure is entirely too noisy to extrapolate anything definitive because the butterfly shapes aren’t wholly accurate (yet). I looked for a few hints on the web and in the Escher books I have but couldn’t find anything analyzing this particular design in the context I need it. So that’s where you come in if you’re so inclined to help. In return  I’ll share anything I come up with as the design evolves.  Thanks everybody!

Related:
Escher paver molds (I may get these for my patio).
How to make pavers
Open source lizard paver pattern.

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