More Generalizations
As was clear from the last section (Some
Circular Designs), one idea for a curve-stitch design often
leads to other, unexpected patterns. In this section, I will describe a
line of thought that led me to devise more designs and to build more
tools for producing them.
Many of my designs (particularly those in
A Family of New Curve-stitch
Designs) have begun with a square. What would happen, I asked myself,
if squares were nested, as shown here:
The triangles at the corners of each square could be
inscribed with parabolas, and this design could be repeated indefinitely, in the
progressively smaller squares. (Such patterns are more suited to
computer-generation than to construction with cardboard and thread, of course!)
To facilitate drawing such a design, I wrote PostScript to draw parabolas on
adjacent sides of arbitrary polygons. Given my immediate objective, I began
using the code to produce triangles, such as would be needed for the proposed
construction:
I quickly realized that I could do more with this
code than I needed for my design. More on this later.
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