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
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
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
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
An absolutely amazing image by Pantone. Sort of puts it into perspective. A quick Google search reveals quite a few of these images, showing the diversity of our skin colour on the planet. A few politicians/clerics would benefit by having their faces added here. 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
There is a very cool feature in iOrnament, the app animates the steps used to create your #tessellations. It is interesting to see the path used to achieve the end result; not always a straight line. I think #MCEsher would have been fascinated! 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
For the longest time, I resisted the need to add more colour, different colours, to my tessellations. I wrote before about this need, Recolouring a tessellation. Here are a few samples of my newly transformed prints. And some notes about my findings on the topic of colour in tessellations. Continue reading
Since M.C. Escher started popularizing “nested shape” tessellations, many artist have dabbled in the field. Some show a passing interest, yet still create with a very deep understanding of the rules of symmetry. Others can’t get enough and create constantly in this medium. Still other artists push the boundaries and explore off-spurs, into fractals, circle limits, non-repeating planes, animation, metamorphosis, pentagonal rules, morphing shapes, platonic solid tessellations, architecture, art shows, consumer products… Continue reading
Sometimes, I find it difficult to spend hours tweaking a single outline for a tessellation. I’d rather sketch freely to come up with some ideas. This was the only way to do it, before the edit line/fill function came along in KaleidoPaint. My drawings were messy and close to impossible to change without adding more of a mess on top. Sometimes it was easier just to start over on a blank page. The trick I had found Continue reading
