Abstract
which is called the golden ratio [5] or its reciprocal [4], depending on the author. Almost any discussion oftthe golden rectangle will include the image in figure 1, which is constructed by starting with a golden rectangle, partitioning it into a square and a smaller golden rectangle, and then repeating the process indefinitely. We will refer to any such set as a golden set. Authors occasionally include the golden set in discussions of self-similarity [5, 6], because it is the union of a square and a smaller copy of itself, scaled by a factor of y. Some popularizations of the golden ratio [4, 7] also include examples of truly self-similar, planar fractals to illustrate properties of y. Now the golden set is not truly self-similar, because it is not a union of smaller copies of itself, but it suggests a problem: Can we construct a self-similar fractal made of golden sets?
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