Sandra DeLozier Coleman
My algorithmic designs are generally drawn freehand without the aid of measuring devices or preliminary sketches. From points dividing an imagined circle into approximately equal parts, repeated steps lead to approximations of rotational symmetries. In this particular design, at one point in the drawing process, I made use of a circular object with a hole in the center to assess and adjust the circularity. The points between the center and the circle's edge and beyond were all estimated, resulting in variations in the sizes and shapes of related areas in the drawing. It is interesting that although corresponding areas are not actually congruent, there is "at a glance" symmetry based on elements that are invariant in the design.
At an art show a few years ago, I was encouraged to demonstrate the process of creating an algorithmic design like this one. I was delighted to find that my booth attracted a large number of children who seemed eager to try to create designs of their own. The question that arose most often as they watched me drawing in ink was, “What if you make a mistake?” It always brought a satisfied nod when I replied that this was one expression of mathematics where it is ok to make mistakes, as long the mathematical artist makes the same mistake again and again and again!