5-Zone System

 

The 5-Zone System, a series of paintings and prints, continues Clark’s investigation of 5-fold symmetry. Each of the paintings are constructed from 5 sets of parallel lines called zones. The five zones are derived from the sets of parallel lines that appear in the shadow cast by the triacontahedron (a zonohedron). A zonohedron is a polyhedron in which the edges surrounding each face can be grouped into zones.

In 1970 Clark Richert observed that the shadow of the triacontahedron produces two sets of rhombi (a wide rhombus and a narrow rhombus) that "close-pack" together to tile an infinite plane without forming repetitive patterns. He call the tiling a "quasi-pattern". This non-periodic tessellation underlies the work in this series reflecting 5-fold symmetries, permeated by relationships in the golden proportion (phi).

Quasi Schechtman

2011, Acrylic on canvas, 70” x 70”

 

The phi ratio seems to arise out of the basic structure of reality appearing regularly in the natural world, in things that grow and unfold in steps, including living things. For instance, plants and trees grow in the phi ratio. Leonardo da Vinci understood that humans are constructed in the proportion of phi. In fact, it was recently discovered that DNA itself incorporates phi proportions in its construction.

 
 
5 Zones, 35" x 35", digital print, 2012  

Quasi Moire

2014, Pigmented ink print, 24” x 24”

In 1976, The physicist Roger Penrose devised matching rules to force the "wide and a narrow rhombi" into non-periodic tilings of the plane. This anticipated the discovery in 1982 of the Quasicrystal.

The final painting in the series, Quasi-Schechtman is titled in honor of chemist Daniel Schechtman's 1982 discovery of the quasicrystal. In 2011 he was awarded the Nobel Prize in Chemistry. An article about Schechtman in the February 2012 issue of Chemistry in Australia, reproduced this painting and acknowledged my use in artwork of the non-periodic tiling system in 1970.