Most simple of all symmetry systems. A translation of your design both vertically and horizontally. That’s it! The shape is up to you as long as it repeats in those two directions, and is built around a four sided figure, square, rectangle, lozenge. No mirrors, no rotations, no glides — simply a translation. Straying outside the basic parallelogram is encouraged.
The image below illustrates two simple lines translated both up/down and left/right. Again, as in all tessellations, it up to you to figure out what to place inside the shape. Just like imagining sheep in cloud shapes. Tweak the edges, repeatedly and something might emerge.
Symmetry group p1 = one translation horizontal, one vertical, anything goes
Any shape works! As you can see from the tessellation below. Follow the cat’s tail and see how far you get. A most unusual stamp!
Symmetry Group p1-cat-with-tail-into-the-next-galaxy © 2013 Champagne Design
Sometimes the shapes can be easy to fill, sometimes they can be challenging. The most simple shapes have slight modifications from the basic repeating squares, rectangles, parallelograms. The tessellation below started off fairly easily, the brown puppy repeated by translation.
Symmetry Group P1 – A zoom-out shows the repeating parallelogram © 2013 Champagne Design
The challenge was to fill the rest of the unit cell with something adequate to the topic. Three more puppies. That last white one was a stretch. The tunes by Three Dog Night come to mind, and morph into Four Dog Day.
Symmetry Group P1 – Four Dog Day © 2013 Champagne Design
For a simpler, but still quite pleasing tessellation, the Crashing Waves below are a simple modification to a parallelogram (highlighted). Feels more like wallpaper, wrapping paper than an actual tessellation, but it illustrates the concept well.
Symmetry Group P1 – Crashing Waves – © 2013 Champagne Design
Lots of software out there to help you accomplish this type of design.
An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks.
There is also a java-based program “Escher Web Sketch” at the Ecole Polytechnique de Lausanne. Make sure Java is enabled and not blocked by your security software.
Also, another screen-based software by Anselm Levskaya Escher Sketch v2. (I used to have a basic Mac-based software, way back in prehistory, 1995, by the same name. It worked on the cutesy first Mac)
Or a pair of scissors and a piece of cardboard works quite well. That’s how I learned.
Comments are always welcome!
If you’re a “Learn by Seeing” “Learn by Doing” kind of person, I’ve started creating videos on “how-to” create tessellations. I’ll be covering each of the 17 symmetry groups, one class at a time. And like all artists, we need to make a living. So. I’ve uploaded these to the Skillshare platform. I’ll get paid by minutes watched.
You can take the classes for free. Skillshare offers anywhere from 2 weeks to a month for free if you sign up, even temporarily.
You can register for just a month and cancel anytime. It’s less than the cost of a Netflix subscription!
There are over 40,000 classes on topics for creative persons just like you. Join my mailing list, either here on my blog (in the sidebar), or a at this link for a specific list I use to announce new classes.
I’d love for you to join me on this wonderful learning adventure.
If you prefer, you can follow my progress on social media, I always announce my new class:
Facebook: Franc Champagne, and Vancouver Island Tessellation Artist
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Youtube: Video animations and class intros
Tessellations by Francine Champagne 
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