Monday, November 8, 2010

Amazing Escher Patterns!

I got an email recently from Steve Armstrong, a math professor at LeTourneau University. He uses my GeomeTricks books, and one of his geometry students produced some amazing Escher-like tessellations. The student's name is Garret Robbins, and I uploaded 6 of his models to the 3D Warehouse.

There are some based on rectangles (click a model's images to go to its 3D Warehouse page):


Babies and Monsters (the babies are upside-down)



One tessellation is based on a triangle:

And my favorite is based on a hexagon:

Here's what Garret had to say, on how he came up with these patterns:

I just started with a shape (a square, rectangle, triangle, etc.), and simply drew a few lines here and there on each side, copying them to the appropriate opposite side. After that, I just tried to see what kind of artistic figure I could make out of the shape that I had created. On a few, I adjusted the entire tile to fit more closely to some figure that the tile resembled. Otherwise, it was just random.

I posted a project on the Math Forum last year on how to make rectangular Escher patterns. Go here, and scroll down to October 2009. Triangular and Hexagonal patterns are similar; both involve copying lines and arcs from one polygon edge to others.

Anyone can design anything in 3D!

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