This blog shows two examples of the translation of 60 degree rotational (P3) tessellations to 90 degree (P4) tessellations. Many symmetrical tessellation designs, that is a tessellation with mirror reflection about a central axis, are capable of being transformed from the 60 degree (P3) state to a 90 degree ( P4) form. This doesn't mean that the design will be able to be simply copied just that a form of the design can be modified from one state to another. I thought I would show a couple examples of how this works and provide some commentary on the modifications.
Figure 1 depicts Horned Lizards as a 60 degree rotational design or a P3. The tessellation is rotated 60 degrees and repeated. Figure 2 depicts Horned Lizards as a 90 degree mirror reflection design or a P4. The design repeats at 90 degrees as a mirror refection. Figure 3 shows Jets and Pterodactyls as a 60 degree rotational design or a P3. Figure 4 is a 90 degree reflection of the same design.
There are many symmetrical tessellations that can manipulated in this way. Normally the approach I take is to start with a P3 (60 degree) design and overlay a it on a square grid with tracing paper. I then stretch and create a 90 degree grid with "mirror symmetry" and design around the center axis to complete the tessellation.
The following is an example of how I create tessellation art. I typically start with drawings in a sketchbook similar to the Figure 1. Many times these designs sit for months and even years before becoming a print or drawing.
Figure 1 depicts a tessellation titled "Bats & Birds" from one of my sketchbooks from December 2000! Not all designs take this long from creation to development but this one was definitely longer than most. A portion of this tessellation design was used in creating the image for "The Lost Domain". However there are typically two or three steps in development. First the tessellation has to sized and repeated. Following this step the image needs to be combined with a theme, idea, story or figure and ground within the art.
The image for the Lost Domain had at least one theme that was rejected. Figure 2 below depicts the rejected theme.
My thoughts about the direction of the image changed somewhat during the development. After rejecting the Figure 2 design I recalled a book I had read many years ago entitled "The Wanderer" also called "Le Grand Meaulness(The Lost Domain) ". The book was written by Henri Alain-Fournier in 1913. Unfortunately he was killed in action during World War I. The final image was created from my interpretation of the book. Figure 3 depicts the final version of the image.
Its not unusual for many of my designs go through several iterations before they are finalized.
The final image for The Lost Domain, August 2016. By Michael Wilson.
Michael Wilson has been creating tessellation art for over 40 years and is preparing this blog to share thoughts on the subject.