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.
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
The original tessellation, with Arjen Robben as the “diver” was done in 2016, titled Gelbe Karte, or yellow card in German. I’ve modified it in view of the trend on the net, cats, dogs, mice rolling when they hear the word “Neymar”, even the kids getting in on the action when their soccer coach yells “Neymar”! 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
New word in my vocabulary. Zentangles. Have no idea when this word was invented, but I seem to have been doing something similar since my teen years. Not quite like the three images below as these have a repeating pattern. 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
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.
Hey, nice fish. Do you catch and release? Bit of exageration going on in the drawing as well as in reel life. All bent over and stretched out, imitating the size of his catch, same as stretching reality. Elvis hairdoo. All in good fun. Would be cool to have a long sleeve t-shirt with a measuring tape printed from hand to outstretched hand! 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
My Little Patch of Green.
This tessellation started off as a village of dwellings. Urban. Concrete. Barely a patch of grass. Actually, there are three small triangular lawns in there, but you have to search, like in Waldo. Continue reading
One Tessellation a Day, for 30 Days! Ya, right.
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
The size of the audience for this type of art-form is microscopically small. When you start talking about your tessellation passion, someone inevitably says, “Ah ya you do that stuff”. From decades ago, “oh ya, I remember your drawings”. Other than family and friends putting up with your gushing obsession, you’re lucky to have a handful of patrons. Math teachers, grade school kids, and a few geometry nerds don’t constitute a large client base, lol. Continue reading