End Grain Cutting Board Using MC Escher Tessellations

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Introduction: End Grain Cutting Board Using MC Escher Tessellations

During my residency at Pier 9, I decided to do a project using the Coherent Metabeam Laser Cutter. I've been fascinated by MC Escher tessellations for a while, and in lieu of seeing so many end-grain cutting boards being made, I decided to take it to the next level by making an end-grain MC Escher tessellated cutting board. I chose the lizard pattern because they had a recognizable beauty and complexity of shape that would allow me to push the limits of the end-grain cutting board using the Metabeam Laser Cutter. This is a time and machine-intensive process, but with gorgeous results. I encourage you to find an easier way to to this!

Tessellation Theory: MC Escher developed tessellations after viewing a pattern in The Alhambra and using inspiration from Penrose Tiling. They are based off of a repeating hexagonal shape, where a piece is taken from the inside of the hexagon, and rotated/slid to the adjacent side. This pattern can be repeated until you have a tessellating lizard! View a video of the process here.

Step 1: You Will Need:

1. Maple, Cherry, and Walnut 2x2in 3 foot lengths. I got mine from MacBeath hardwoods in Berkeley. They've got a vast selection of woods. Material cost was roughly $70

2. Titebond 3 Wood Glue, under $10 from MacBeath

3. Coherent Metabeam Laser Cutter

4. FoodSaver Vacuum Sealer & Bags

5. DMS 5 Axis-Router, Bridgeport Mill, or CNC Shopbot

Step 2: Laser Cutting Tessellated Lizards

This was a tricky procedure. I wanted a 1/2 in cutting board, and only the Coherent Metabeam 400W would cut it (pun intended). The software is very antiquated and it took some time to figure out the right offset. Tessellations are difficult, because any variation will either cause the whole thing to have slack, or as you add more, it'll lock up on you. Trial and error is the only way to do this. Cut 9 with one offset, and cut another 9 to see the difference. Iterate, Fail. Burn lots of wood.

Testing The Tessellations:

This needed to be taken into account when testing the offset. The shape was MUCH tighter on one side than the other. I found a .045in offset on the whole lizard allowed them to lock together sufficiently.

Next, I needed to cut 3 different hardwoods, each with different densities and flash points. It took a lot of trial and error to get the power and feed right.

Lasers are a high-precision tool, but have a kerf width that is shaped like an hourglass. This is very apparent when looking at the reverse side of the assembly, as the gap is completely closed. I had to use a .2in focus offset to get it to burn through.

Making A Jig:

I cut a jig out of acrylic to house the 2x2in squares. I used the DXF from the jig and placed a lizard within the file, and repeated the pattern. Please Note: Don't move the jig, and make the lizard within the same file, so that the origin stays fixed. Or make alignment holes so that the cuts don't fall out of alignment. I made this mistake and it took quite a lot of work to manually find the right orientation.

Production Run:

Once the jig is aligned, and you know your laser settings, it's time to do the production run. Lay out your blocks within the jig, and modify the final cut file to accommodate the number of blocks you are working with. Sit patiently as the lizards are cut out, keeping an eye out for fires or the cuts running off the wood.

Step 3: Filling the Cracks With a FoodSaver Vacuum Bag

Once the lizards were assembled, I needed to glue the cracks. The kerf width didn't allow for a completely flush fit on both sides, so the options were to either glue and assemble the piece manually, or let vacuums do the grunt work. We had a FoodSaver in the test kitchen, so per fellow AiR Robb Godshaw's suggestion, we put it in.

I diluted the glue so that it would seep into the cracks, poured it in, and let it sit for a few days. Air bubbles would pop out from between the lizards. Letting it cure for a week was optimal, as the glue became tacky due to the presence of the air bubbles.

There was a surprising negative volume between the cracks, so it took two packaging runs to get the board whole.

Step 4: Planing the Board on a DMS Router

I needed to plane the board, which had a 1mm thick layer of wood glue left over from the gluing procedure. I couldn't use the planer in the Pier 9 Workshop, because the bit would take chunks out of the end grain, and shatter the board. I also couldn't use the Supermax drum sander, because the wood glue would ruin the sander.

We have access to a DMS 5-Axis router at Pier 9, and I had taken the class earlier that day, so why not get some practice on it? I used an end-mill bit to perform a facing operation manually. I could have programmed something, but it was much simpler to use the manual jog in the X and Y axes to perform the facing.

It's just like mowing the lawn, with an incredibly precise machine. It might have been overkill, but I couldn't find a simpler way. You could use a Shopbot, or even a Bridgeport mill. The trickiest part was mounting a vice with parallels to keep the wood where I wanted it.

Lessons learned: Never plunge when using an end-mill! I stepped down in the Z axis with each pass, but should have gone more slowly with each pass. The end-grain chipped a tiny bit and it took a bit of sanding to fix it.

Step 5: Hand-Finishing & Sealing the Piece

It took a bit more manual glue to fill all the cracks, so that had to be sanded off. I took an orbital sander and sanded it smooth on both sides using 60, 80, 120, 220 grit successively. Then I used a sander block to round the edges.

I sealed it using mineral oil and a rag. And it made it pop!

It's so pretty, i'm not sure if I want to cut on it...yet.

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thanks for sharing it here. that's very nice and professional. have a good time.

I recommend sealing with walnut oil and sanding the surface with ultra fine steel wool a few times before using mineral oil. Walnut oil will actually cure into a solid varnish and actually seal the wood. mineral oil doesn't cure into a solid coat.

Unlike linseed oil, Walnut oil cures somewhat slowly and isn't yellowish when cured.

Also look at Tung Oil, the real stuff, not Tung Oil Finish. Mix the Tung Oil with Lemon Oil solvent (about 50/50) and soak the whole board in it. Then let it cure for a week or so. You can then do a layer or two of straight Tung Oil if you want, but I don't think it is necessary.

It makes the grain really pop, it is food safe, easy to find at woodworking stores, VERY waterproof and you can later use any food safe oil you want on it to touch it up. Over the years I have fallen in love with Tung Oil for lots of reasons, not the least of which is that it is one of the best finishes for stabilizing wood against swelling. I live in Florida and that is a huge consideration for me.

I think it would be great for your cutting board.

Congrats!
What a wonderful job you have done, :)
I´m also a Escher fan, reading about tessellations I´ve done many drawings but
Eschr´s lizzard always was elusive, even following the vid on Youtube.
Illustrator files are already downloaded, thanks for sharing. By the way... do you have nore Escher´s animals or tessellations into .ai files to keep sharing?
fmorocho@yahoo.com

Dear Light_Lab, regarding "word to the wise". M C Escher knew of the Penrose stairs, created by Lionel Penrose and his son Roger. Roger Penrose was inspired by Escher's work, which he came across in 1954. The pair came up with the Penrose triangle, or impossible triangle. Roger then developed the never-ending staircase, using more than one impossible triangle. He presented it to his father who then produced more variants on the theme. They eventually published their work in 1958 in the British Journal of Psychology because Lionel Penrose knew the editor. The Penroses sent a copy of the article to Escher who wrote back to the Penroses in 1960. In that year Escher produced Ascending and Descending - his famous never-ending staircase and in 1961 Escher produced Waterfall clearly using 2 Penrose triangles. Escher was clearly inspired by the Penroses work, so they both inspired each other. Incidentally, the impossible triangle and stairs had been previously invented by a Swedish graphical artist but the Penroses, & Escher, were unaware of this at the time.

Thanks for reminding me, I have been working so long with Roger's work I had almost completely forgotten completely about Lionel's work. I knew Escher had interacted with other mathematicians but I was not aware of the connection with the Penrose family; thanks for that information. Nevertheless it still remains that Penrose Tilings are named from Roger's magnificent work on asymmetrical, non-repeating tilings.

I confess to being more involved with developing algorithms than history or biographies; but you have sparked my interest. From which reference did you obtain your historical information?

Thanks for the added dimension. Much appreciated.

Trouble I would have is that I couldn't use it for its intended purpose and it would be on show! Lovely.

Gosh, I wouldn't want to cut on it. As a M. C. Escher fan from way back, I would mount it on the wall to admire, not cut. Beautiful work.