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
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
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.
This tessellation was done using the Pg symmetry system. Two parallel glide reflections with a few lines snaking from one to the other. In the sketch below, the thicker lines delineate the two characters, the guy and the dog. Not that many lines. The thinner lines add details to the shape. If you want to know an easy way to create this type of nested shape, have a look under the Techniques menu, and choose the symmetry group you would like to use. 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
It has taken a while for me to let go of the expensive Adobe Photoshop, to complete my tessellations. Quite a bit of research and testing to figure out which iPad app was the best for my purposes. Pixelmator wins on all fronts. It does what no other single app accomplishes, Continue reading
Below is the original OmegaBoy sketch, drawn four and a half years ago already. Since I found the KaleidoPaint app, I’ve come up with about one nested shape a week, that’s over 250 tessellations, fully interlocking designs. It must be an obsession! Still much to learn. Never stop learning. Continue reading
These ocean-side tessellation topics are dear to my heart since we moved to the Island, a decade ago already. The weather is wonderful, winter and summer, those year-round hikes — local, beautiful, plentiful, varied. Continue reading
I had a quick look through all of my #tessellations from the past years and came up with a list of 30 “Family-Friendly” topics. Most of these are from the animal kingdom. Safe topics for the kids. And many kids encounter the art of tessellations either through their art class or their math class in grade school. They relate to the art style quite well. Continue reading
A new App called “iO Crafter” on the iPad has just come out, from Jürgen Richter-Gebert. Using it to deform into spirals is where my interest lies. As well, it has other functions to deform your images: build a platonic solid; build a kaleidocycle; view a kaleidoscope; hyperbolic kaleidoscope; and conformal maps. Continue reading