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.
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AuthorMichael Wilson has been creating tessellation art for over 30 years and is preparing this blog to share thoughts on the subject. Archives
May 2018
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