verb (used with object)
1. to form of small squares or blocks, as floors or pavements; form or arrange in a checkered or mosaic pattern.
Source: Dictionary.com Unabridged
Our goal for this Indestructibles project was to create approximations of M.C. Escher’s tessellating lizards using a laser cutter. While working on this project, we learned about the math behind shapes that interlock, how to programmatically create SVG (Scalable Vector Graphic) files and a few new tricks on the TechShop laser cutters.
Step 1: Get Inspired!
Step 2: Getting the Rough Shape of the Lizard
Step 3: Correcting the Vertices
We first adjusted vertices 8, 26 and 42 to ensure that they do form an equilateral triangle. We then created three additional copies of the lizard in Matlab to check how well the pieces would interlock.
You can see that the edges don’t quite fit. No problem… We adjusted the coordinates of the black lizard’s left cheek and left shoulder, for example, to exactly match the green lizard’s face. As long as one carefully keeps track of which vertices are moved, these adjustments lead to lizards that will perfectly interlock.
Step 4: Trimming the Lizard
Step 5: Creating the SVG File
Our Matlab script created an SVG file with three sets of three interlocking lizards. The image above shows the resulting SVG file loaded into Inkscape.
You may notice that the lizards are mirror images of the ones we started with. This is due to a difference in how Matlab and SVG understand Y coordinates: Matlab places Y = 0 at the bottom of the page while SVG places it at the top of the page. No worries… We can simply flip the pieces over once we’ve cut them!
Now off to the laser cutter!
Step 6: Laser Cutting!
Step 7: Choosing the Material
Since all laser cutters are different (not to mention that there are even variances between laser cutters of the same model), it is best to start with a practice cut on a spare piece of the material. I typically cut a series of small geometric shapes until I find the settings that give me the desired effect. For our purposes, we were only using vector cuts and the following settings worked fine for us:
* Speed = 25
* Power = 90
* Frequency = 500
As a side note, my favorite laser cutting trick is to cover the cutting surface of the material with blue painters tape - it allows for a nice clean cut and it prevents scorching. When the cut is complete, the blue tape comes off with relative ease.
The image above shows the cut-out after it was scaled down by 25% in CorelDraw. This demonstrates the benefit of scalability when using vector graphics.