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.
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
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
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
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
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
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
This tessellation is built using the Pgg symmetry group. A grid of two different perpendicular glide lines with two different two-way (180*) rotation points in the middle of each rectangle. Sounds like a lot to take into account, when planning the drawing, but it’s not that difficult. Continue reading
I’ve chosen a pattern from an Islamic geometric design as inspiration to get started for this tessellation. Looking at the photo, we can see four mirrors intersecting at ninety degrees to form a box. In the centre, a four way rotation point. Continue reading
My first ever tessellation, redrawn from scratch, to show the series of steps required to achieve a successfully nested shape.
The original image was a pencil sketch from years ago. Before Windows 3.1 and way before the iPad. And I could not afford an Amiga computer, even less the first Mac. So cardboard, pencils, scissors and lots of graph paper it was. Continue reading
This tessellation is built using the Pm symmetry group – two alternating parallel mirrors, without any glides or rotations. Makes for a stacked look to the nested shapes. One vertical mirror down the lady and the other down the dog and shampoo bottle. Always wondered how HairStylist cut their own hair, awkward to cut your own, probably dangerous too. Well, I figured it out. “Let me cut my hair for me”. And it’s always nice to bring Fifi the dog with you to the Salon. What do you think Tina? Continue reading
Indeed, not my favourite symmetry group. Most nested shapes that try to fit into this system feel constricted, weird, rigid, way too symmetrical. There is barely enough room to create recognisable figures within a sliver of a triangle, 30-60-90 degree (orange shape). And all of this surrounded by 3 mirrors. Ug. Continue reading
The other side of me is the carver, 3D instead of digital artwork. I came across a carving by Chouki Derrouiche, a tessellation of Whirling Dervishes carved with different woods. Spectacular. I undertook to figure out which symmetry system Chouki used to create his nested shapes. I was baffled as to which symmetry system was being used Continue reading