My fascination with tessellations started with a book purchase. M.C.Escher. The master of tessellations. If you don’t know MC Escher drawings, Google it for images. He was quite popular with the drug-induced hippies of the sixties. He created scenery lithographs, weird incomprehensible worlds and tessellations. This last one kept me mesmerised.
Being fascinated and totally understanding something are quite different beasts. My understanding occurred during a class on “the nature and behaviour of materials”, at the architecture department at Carleton U. Prof Westwood was talking about the atomic structure of materials, their strength ratios, breaking points, critical crack lengths… daydream inducing topics till he hit the section on crystallography and the 17 possible ways of assembling identical shapes. Blew my mind. He had made the link for me to understand tessellations. The same rules apply to creating seamless patterns.
Started off doing seamless patterns by hand, the same way Escher did. Sheets of paper, ruler and pencil, sometimes helped with a cutout of the shape to be repeated and traced. Tedious but rewarding.
Just this year, I found an iPad app that does the same, but in record time! KaleidoPaint by Jeff Weeks. Blowing my mind again. Visit his wikipedia page: Jeffrey Weeks (mathematician) as well as his website and image gallery.
Here are a few images I was able to create using this new iPad app.
A view inside an equilateral triangular surface surrounded by 3 mirrors with a 3 way rotation right in the center. Of course, you can place anything inside the triangle, the trick is to place something that is recognisable, seamless, and preferably no blank space. Manta Rays in this case.
This second image is also a triangle, isosceles, but with crossed mirrors at the 90 degree right angle corner and a dual rotation point at the middle of the hypotenuse, the long side of the triangle.
This third image is based on a view inside a square, 4 mirrors without rotation. The repeating area starts in the middle of the beaver, up to the green suited figure’s eyes, down his body to the spot between his feet, down through the moth’s body to the middle of the mosquito and back to the beaver. No, I’m not on drugs!
These are just 3 examples of the 17 systems you can use to divide a 2 dimensional surface. Billions of possibilities. Hope you enjoy creating your own tessellations. Comments are always welcome.