These designs have a common motivation. I have always been intrigued by repeating patterns. Whether wall paper, wall tiles, or the bathroom floor, I would sometimes stare at the patterns or tiles with great concentration. Maybe it was like looking at a mandala. A form of meditation. I would try and create more complex designs out of the simple patterns present by imagining connections among the parts.

One way to create complex designs is to use recursion. Recursion is a method of extending a simple pattern by replacing some part of the original pattern with the entire original pattern, but drawn on a smaller scale. The new pattern made from this process still contains the original pattern, so the operation can be repeated again and again, each time yielding a more complex pattern.

One example of this is the picture in a picture. The picture is of an artist's studio with the artist painting a picture on an easel. The picture on the easel is the original picture. Another common example of recursion is to stand between two mirrors held parallel to each other. One sees in infinite number of reflections of oneself.

By its nature, recursion is infinite, and real pictures or designs can only show the recursion up to some limited point. But usually the mind's eye can look at the limited recursion and see the infinite pattern. This makes a good way to meditate.

I chose needlepoint for these projects for many reasons. I wanted to end up with pictures to hang on the wall to be viewed from across the room. I wanted durable construction that was low maintenance. I considered mosaic, but the amount of detail possible was low unless a very large project was undertaken. Making a mosaic out of small colored beads remains a possibility for future projects.

I was introduced to needlepoint by my mother, who had made many beautiful designs based on M.C. Escher's work. I tried an easy project, and found needlepoint very relaxing. The results looked good, even though I was a beginner.

Each of these projects took a year. I would typically design a new pattern during the holiday season. In February I would buy the yarn and canvas. Doing the actual stiching lasted from March thru November.

I studied mathematics and computer programming, so part of the fun I had was in constructing programs to create the designs, color them, and render them as needle point patterns. These designs are based on one of three different patterns: Pentominos, Fractals, or two forms of the Penrose tiling.

you need to use many sets of the twelve shapes. The easiest way is to fit them into the frames mentioned above, then arrange these rectangular frames into fill the area desired. However, if you do this, you immediately see the outlines of the frames. I wanted a pattern that would not easily reveal boring rectangles when I looked at it. I wanted to use an equal number of each shape. I wanted each shape evenly spread out.

The answer ? Recursion. Fit the twelve pieces into twelve frames each shaped like one of the pieces themselves. This project is one of many designs I made on this theme. The colors chosen match a couch in our living room.

I think this approach can be used best on large rugs. I hope one day to hook a large rug based on an even more intricate pattern of pentominoes.

I wanted an example of this to contemplate. This design is the result. The coloring emphasizes small symmetrical areas, as well as highlighting the non-symmetric connections between them. One can pick out larger symmetries, and is left imagining how these larger symmetries are connected.

Many computer programmers interested in graphics have written a fractal design generator for themselves. I spent months with mine, exploring the many depths of the "Mandelbrot Set" (A particular type of fractal named after the author of the book.)

I found this pattern in the Mandelbrot Set at a magnification of about 4,000,000 near the location (0.43, 0.22). It looks like an image of a far galaxy taken by a large telescope. You can see at least three levels of recursion in the design. The larger galaxy has many smaller satellite galaxies orbiting it. These smaller galaxies have their own satellites, etc.

Other parts of the Mandelbrot Set have an entirely different apperance. There are many beautiful designs here awaiting only time and effort.