ABSTRACT. . In his fascinating book “Wonders of Numbers”, Clifford Pickover introduces the Ana sequence and fractal, two self-referential constructions arising from the use of language. This paper answers Pickover’s questions on the relative composition of sequence terms and the dimension of the fractal. In the process, it introduces a novel way of obtaining fractals from iterative set operations. Also, it presents a beautiful variant of the Ana constructions involving the golden ratio. In conclusion, it suggests ways of constructing similar fractals for the Morse-Thue and “Look and Say” sequences.
Download the paper (File: anagoldenfractal.pdf, about 36 Kb).
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©2002 J. L. Pe. Document created on 14 March 2002.
