Symmetry Group P4

I’ve already given you a foretaste of this P4 symmetry group with the cougar tessellation, and story, a few weeks ago. A thrilling event, possibly once in a lifetime. If you haven’t read it yet, do. But now for the technical side of this P4 group, with a few more examples.

Symmetry Group P4 – © Champagne Design– Try Running in Workie Boots!

Symmetry Group P4 – © Champagne Design– Try Running in Workie Boots!

Workie boots are heavy. Steel toe and sole. Ever try running in a pair of those?

Symmetry groups P2, P3, P4, and P6, have evolved into my favourite symmetry groups. Possibly because the constructions have no mirrors in them. There is fluidity and freedom in these symmetry groups. You are encouraged to stray outside the mesh limits. Fish-eye lens exaggerations usually occur in my case. (Did you know you could get a clip-on fish-eye lens for your iPhone? Oh, so cool.)  In the case of symmetry group P4, there are two different 4-way rotation points, one inside the box and one outside the box, and four identical 2-way rotation points on all corners of the box (mesh). The image below has these points highlighted. I’ve drawn in a faint red line to outline the box/mesh.

Symmetry group P4 – © Champagne Design – Chicks

Symmetry group P4 – © Champagne Design – Chicks

Point A, the 4-way rotation is linked to one of the 2-way rotation points (C) with a line, the red one. The second 4-way rotation point B, links to anywhere on the first line. These two wavy straying lines will give to a single repeating shape. As in all tessellations, the trick is to tweak the outline, then fill the region with a recognizable figure. Any shape can also be subdivided into any number of figures, if two creatures become apparent to you within your shape, go for it!

The sketch below, has the same structure. Four identical 2-way rotation points, at the rump, and two different 4-way rotation points; one at the ear and one at the front hoof.

Symmetry Group p4 – © Champagne Design – You Talkin' to me?

Symmetry Group p4 – © Champagne Design – You Talkin’ to me?

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.

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! And you can still stay put on the couch. 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
Instagram: champagne.francine
Twitter: FChampagne1
Linkedin: Graphic Design, PowerPoint and tessellations
Youtube: Video animations and class intros

My classes have received an independent rating of 9.7/10, placing these Skillshare classes in the TOP 2% of classes reviewed by CourseMarks!


Rekindle your Love of M.C. Escher Tessellations, draw your own tessellations using a free iPad App rating

Here is a list of the classes up so far:

  1. Rekindle your Love of M.C. Escher Tessellations, draw your own tessellations using a free iPad App. In this class I introduce the concept of tessellations, show you the work of M.C. Escher as well as other artists. Then we dive into a first symmetry method, P4g, accomplished by drawing only one line to create the perimeter of your tessellation.
  2. Just like M. C. Escher’s Tessellations: Draw Using a New Symmetry Method and Your iPad. We tackle the Mirrored Triplets symmetry group, aka P3m1.
  3. This UP/DOWN, LEFT/RIGHT Tessellation method was M. C. Escher’s favorite. It is also the symmetry method, P1, most taught in schools. Probably the only way most artists have tried to accomplish a nested shape. We will push it a tad farther, but also easier than scissors and cardboard.
  4. M. C. Escher Tessellations: The Three Cozy Buddies Symmetry Group, know as symmetry group P3. Lots of examples, from many different tessellation artists. One of my favorite ways of creating tessellations.
  5. Digital Patterns: Super Simple Quickie Patterns. 20 patterns in 30 minutes! I will show you how to draw and assemble your pattern design elements in four different and unusual ways. Come explore the possibilities, from a different point of view using your iPad and the free KaleidoPaint app. There is more to symmetry than rigid repeats, half-drops and tossed layouts.
  6. My next class with deal with a symmetry group I have named: “This way — that way”, aka crystallographic notation Pg. That Koloman Moser video above, is part of the series.

2 thoughts on “Symmetry Group P4

  1. Pingback: Symmetry Group P4 | champagnedesign

  2. Pingback: KaleidoPaint iPad App Help | Tessellations by Francine Champagne

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