I have been working with needle crafts since graduate school. I have also been interested in fractals and fractal geometry for more than 25 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 the website Gasket Fractals by Robert Fathauer. The black right triangle in the upper left corner is divided into 9 similar right triangles. In the first two images, 2 triangles are removed as shown on the left and the construction is iterated on the 7 remaining right triangles. In the bottom two images, 3 triangles are removed and the construction is iterated on the 6 remaining right triangles. The images on the right show the results after 5 iterations. The different colors in the four images are used to illustrate the self-similar nature of the resulting fractal. Each of the individual colored pieces is a scaled copy of the fractal. These are just four of the 280 possibilities, not counting reflections.