This list is to help you get started in creating your own nested shape tessellations. I’m not showing you how to create wallpaper patterns with lots of free space in between, but the true, à la M.C. Escher designs. A tessellation of a flat surface is the tiling of a plane using one or more fluid shapes, called tiles, with no overlaps and no gaps. Continue reading →
There are three of them living under this ruff. They own the place. Yahoos when they are not gate guardians. Named this one Bibi, possibly for bierbelly. It is based in symmetry group P3 and the pentagons of Type 3, a hexagon split three ways. It’s a stretch from its original lines, but that is indeed where I started. Quite a simple tessellation with only a few lines. And a favourite tail twirl around a three-way rotation point – I’ve done that one quite a few times. Continue reading →
My Pentagon Challenge is keeping me busy. I am plowing my way through all of the pentagonal tiling types. Quite a few of them are built within either a perfect hexagon, or one that has been distorted beyond recognition. I am finding some interesting rules of symmetry I had not yet encountered. Wrapping my noggin around new concepts. Many of these symmetry types are skew-able, not only scale-able. Also, many of the anchor point for division lines inside hexagons are variable in their location, as long as the variable is kept constant for each pentagonal unit. Continue reading →
Another challenge showing up on my desk, compliments of Woodpecker Carving. Hussein posted a beautiful Islamic geometric design, displaying the use of pentagons. But wait I thought, aren’t pentagons impossible to tile using the original seventeen symmetry groups? Or so I thought. I had seen intriguing examples of pentagonal tiles over the years, but I was still obsessed with M.C. Escher type nested shapes – and will always be. Continue reading →
A PenDragon, a dragon tessellation emerging from a pentagonal tessellation. It took a while to complete the final colouring, texturing and shading on these three dragons. They were created using the P3 symmetry system, while I was working through the tiling of pentagons, using the App KaleidoPaint. Continue reading →
This one is going to take quite some time to complete. Stay tuned! It started off as an exercise in tessellating pentagons. Not an easy task. It took mathematicians over a 100 years to figure out all of the ways it could be accomplished. Good article about pentagons on the Quanta Magazine website, check it out. Continue reading →
This Mountain Biker #tessellation drawing was done before Windows 3.1, before the Mac, before iPads! But after the dinosaurs. 1997. It was the inspiration to do a complete periodic drawing covering the plane, rather than a line group as shown below. Sometimes these drawings take time. Tessellation ideas are a dime a dozen — completed artwork is more rare. Continue reading →
All this talk about sharing space between characters in a tessellation has made me think of the word “symétruc”, which I coined a few years ago in a discussion with Jeff Weeks, American mathematician and KaleidoPaint app programmer. My original intention was for a word better than the French “pavages”, or “dallages”, which to me aludes to floor tiles, patio stones or asphalt pavement, rather than graphic art. Tessellation can be used in French, I’ve since found out. Continue reading →
On the theme of ‘multiple sharing’ (as with ‘Mountain Biker’), are you familiar with the work of Raoul Raba in Zoo Mathématique? He has occasional examples. As a concept, there are not too many artists using this idea in their tessellation work. The premise of ‘economy’ is a pleasing one. Continue reading →
Yes, another mountain biker. But this one drawn in symmetry system P6, that’s one 6-point rotation, one 3-point rotation and one 2-point rotation. Have a careful look at those bike wheels. They are being shared by multiple bikers. Bike Sharing, very popular these days.
Clocks back one hour tonight. Spring forward — Fall Back. This symmetry design is built using a simple glide reflection all the way along the line. Resting dogs, using their buddy’s butt as a pillow. Continue reading →
I will be showing some tessellation prints at the Board Game House in Nanaimo, for the next two months. Hanging of the artwork is October 28, 2017 – the show concludes at the end of December. Come see. Widen your perception of the fine line between art and math. Stretch your imagination with a bit of geometry, symmetry. Humor and funny characters too. Continue reading →
I thought maybe it would be a cool idea to challenge myself to do a tessellation a day for 30 days. Maybe in a few decades when my teacup is not overflowing.
I must point out the difference between a tessellation and a pattern, as in cloth, tiles or wallpaper. They both use the same symmetry rules for filling space. But in the case of tessellations, your aim is to reduce negative space, empty areas, to zero. Where every single square inch is used up by a recognizable figure. Continue reading →