I have been working with needle crafts since graduate school. I have also been interested in fractals and fractal geometry for more than 20 years. I have I combined these mathematical and artistic interests to create cross stitch and backstitch 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.
The Levy Dragon Outside Tapestry consists of four copies of the Levy Dragon built from the edges of a square. The iteration steps are repeated on each of the four sides of the square with the initial triangle motif placed outside the square. This back stitch design shows the twelfth iteration for this outside construction.The outside tapestry was done in two shades of blue to better show each of the four copies of the Levy dragon.
The fractal now known as the Levy Dragon was first studied by Paul Levy in 1938, well before computers were able to draw the image or the name "fractal" had even been invented! The dragon is constructed from a line segment with a basic motif that replaces that segment with two sides of an isosceles right triangle. That motif is then repeated on each of the new sides of the triangles. The Levy Inside Tapestry consists of four copies of the Levy Dragon built from the edges of a square. The iteration steps are repeated on each of the four sides of the square with the initial triangle motif placed inside the square. This back stitch design shows the twelfth iteration for this inside construction.