M.C. Escher’s Lizards are by far the most popular of Escher’s tessellations. It can be seen gracing many multitudes of surfaces, legally or illegally. From tattoos, puzzles, belt buckles, car wraps, flooring or landscaping stones… My initial introduction to tessellations was through redrawing this lizard in its nested shape during a class on crystallography at Carleton U. That was a few decades ago, in 1988. But, as I keep on repeating (no pun), to draw a tessellation or to truly understand the structure behind it are two different things.
Combining my two loves: Tessellations & Carving
Sketched this Manta Rays tessellation five years ago. Love its simplicity. One single line connecting the center of an equilateral triangle, repeated in 60 degree increments to the three corners of the shape. This tessellations falls into symmetry system P3. I have many more articles about wood carving on my other blog, www.champagnedesign.com. It is a fascinating field to explore.
Most of us learn the easy/best way. Look at the masters, follow their path and learn all that we can from them. Replicate their artwork. It is a long process, especially without any direction or assistance from a teacher. This is where I’m at right now — copying / learning from the pentagon symmetry system seekers: Reinhardt, Kershner, James, Rice, Stein, Mann, McLoud, and Von Derau. As I did for a while, copying M.C. Escher’s tessellations, decades ago, although I no longer need MCE inspiration to create a tessellation. Continue reading
Create your own tessellation
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
I was approached by a student a few months ago — he was writing his dissertation and needed examples to illustrate the seventeen symmetry groups: 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
Lots of reasons to celebrate!
- A dozen cat tessellations, created between 1988—2018.
- Post #150 on my tessellation blog.
- A new year, 2018, year of the dog. Let’s entertain them. What better way to entertain a dog, than dangle a cat in front of it. Just kidding.
- 10,000 hits on this site, just a few weeks ago.
- My first tessellation ever, was drawn by hand 30 years past, January 1988.
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.