Tutorial Introduction

     In the hope of finding a way to illustrate the possibility of how interwoven designs have been created by artists in various eras and places over many centuries, it is my theory that perhaps these complex designs, in some cases, simply designed themselves.

          The idea is this:  A “Seed Polygon” is copied, as in tessellations or tiling, (placed juxtaposed to the original or a new seed), and the result is more complicated and even more unique than the original.  Hence, the original designs morph into a unique and different design.  The most important thing to remember initially is to take a moment and view the 2D drawing until your imagination shows you clearly what the 3D pattern is.  Until one does this, most of these drawings will appear to be just random lines.  But once your imagination shows you the 3D pattern, it will be difficult to see it in 2D again.  I call them Pretzangles.

         For example, in the case of snowflakes, crystals or fractals, one observes a geometric pattern clearly building itself.  It may be presumptuous of me, and I’m sure there will be a great many people who will disagree with me, but I’d like to suggest that Pretzangles are examples of  ‘Fractals Without Equations’.

         I would like to take this opportunity to thank Steve Abbott for all his fine work in helping to make this Pretzangles Project a reality, and to thank my young nephews, who in 1975 said: “Hey Unk, your triangles are weaving, like the top of an apple pie!!” which was the ‘Eureka Moment’ which started all of this, and also to thank my daughter,  Mary Beth, for her excellent advice and generous encouragement over these many years.

      I’ve included some examples of a few typical PRZ files and have attempted to show how they morph into designs quite different from the original “Seeds” in the Sample Section.

     You can EMAIL me at [email protected] or write to:

Matthew Kells

PMB 410

111 East Dunlap Ave

Suite #1

Phoenix, Arizona


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