Quasi-Periodic CrystalsCrystals are the structural units of minerals on the atomic scale. Traditionally, a crystal has been defined as a solid with a regularly repeating internal arrangement. In three-dimensional packing or two-dimensional tiling they combine into solid masses or extended surface patterns without empty intervals. In the 1970's the British mathematician, Roger Penrose, devised and presented a new, groundbreaking theoretical possibility, that of quasi-periodic (partially repeating) crystals which, contrary to the above definition, overlap and rearrange their parts.They are not simple repeats. The resulting pattern is comprised of two specific parallelograms, five of each. In 1984 the Israeli scientist, Dr. Dani Schectman, astounded the scientific community by producing an aluminum and manganese alloy based on five-fold symmetry. Shortly thereafter, other discoveries were made that have opened up entirely new possibilities in a diverse range of technologies. Aside from their visually interesting morphology, a special attraction of QPC for me is the exciting fact that that the proportions of the Golden Ratio are a determining factor in their organization. I first applied QPC as a pattern on one of the walls of "The Open Receptacle" in 1992. Later, on the computer, I discovered an Islamic-type method based on pentagons. |
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