# Larry Riddle

Professor Emeritus of Mathematics

Agnes Scott College

Decatur, Georgia, USA

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.

Right Triangle Divided by Nine

50 x 40 cm

Cross stitch embroidery on 28 count canvas

2019

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.