My first ever tessellation was accomplished using this P4g symmetry group.
My understanding occurred during a class on crystallography, works with the same principles. What a blast that was. Hooked since then.
The basic concept is a 4-way rotation inside a square, built of mirrors. One line from the rotation point to the perimeter corner will give you four halves of an identical figure.
If two lines are drawn from the rotation point, to anywhere on the perimeter, two figures will appear, such as in MCE’s Angels and Devils, below.
Quick identification method for symmetry group P4g:
1- mirror symmetry down the body,
2- figures are head to head and feet to feet, hooked at the arms/elbows/hands/wings…
3- 90 degree rotations at the arms… always end up looking the same, in my case anyhow
The image below illustrates the two lines to the perimeter concept, Two Fitness Styles, one dude posing his bodybuilding skills, the other doing his yoga thing. Note the area sharing for the heads! I seem to be doing a lot of that.
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!