I have been working with needle crafts since graduate school. I have also been interested in fractals and fractal geometry for more than 30 years. I have combined these mathematical and artistic interests to create cross stitch and back stitch pieces to illustrate the beauty and mathematics of fractals associated with iterated function systems. As a mathematician I like to seek fractal images that have symmetry or illustrate some interesting mathematical idea. I must be sure that the fractal can be represented accurately on a canvas that permits only vertical, horizontal, and diagonal stitches of a fixed size. Fractals that are built from squares or from lines rotated by multiples of 45° work particularly well.
This piece was inspired by Tara Taylor's Bridges 2018 article that demonstrated how the convex hulls of symmetric Sierpinski relative fractals can be tiled together to form frieze patterns. The artwork uses 5 iterations of the Sierpinski triangle and three symmetric Sierpinski relatives to form four frieze patterns. The first and third friezes have translation, vertical reflection, glide reflection, and 180 degree rotational symmetries. The second and fourth have only translation and vertical reflection symmetries. The colors in each frieze help exhibit the self-similar nature of the Sierpinski relative fractals. Videos of the symmetries in the four frieze patterns can be viewed at https://larryriddle.agnesscott.org/ifs/JMMVideos.htm.