New Curve-stitch Designs

I began making curve-stitch designs in junior high school, having been introduced to them by my math teacher, Mrs. Eunice Williams. I quickly graduated from using pencils or ballpoint pens to using drafting pens and India ink on drafting paper. Drawing these figures was satisfying but mind-numbingly tedious. Mistakes could be corrected but only with difficulty. Some people, even more masochistic than my teenage self, produce designs with thread, yarn, or wire on a substrate of some sort. More power to them.

My enthusiasm for curve-stitch designs was rekindled by my discovery that I could produce designs using my computer. Frankly, doing so can be tedious as well, but at least it’s not as physically challenging. Using the computer allowed me to post some of my designs on my Web site and even see them published in China and Australia. I have lately been updating Lionel Deimel’s Farrago and have again begun to create curve-stitch images.

In many ways, my favorite creation is what I call my curve-stitch isometric cube. I too an isometric cube and drew curve-stitch parabolas on all adjacent sides. A framed version of this design hangs in my hallway. It consists of white lines on a black background. Here is a black-on-white version:

I have produced my designs by programming in PostScript. a page-description language designed by Adobe. While updating my Web site, I decided to simplify the code that generates the above image. In the process, I realized that I could generalize this design. My cube has six sides. Here is an analogous design with four sides.

And 8 sides:

And even 10 sides:

Well, I asked myself, is it necessary to have an even number of sides in the figure. Whereas in all the above figures, curve-stitch parabolas are inscribed in quadrilaterals. If the enclosing figure has, say five, sides, a triangular area is left over. Why not, I thought, fill the triangle with parabolas. Here is what results of using this procedure on a pentagon:

I also rotated the figure to emphasize its symmetry. Here’s the nine-sided version.

Here’s a final design for fun based on a 20-sided polygon. To keep it from seeming too black, I reduced the width of all the lines slightly

I challenge anyone to reproduce these designs using actual string!