Given an Infinitive Sequence with associated array , then is said to be a fractal sequence

- 1. If , then there exists such that ,
- 2. If , then, for every , there is exactly one such that .

If is a fractal sequence, then the associated array is an Interspersion. If is a fractal sequence, then the Upper-Trimmed Subsequence is given by , and the Lower-Trimmed Subsequence is another fractal sequence. The Signature of an Irrational Number is a fractal sequence.

**References**

Kimberling, C. ``Fractal Sequences and Interspersions.'' *Ars Combin.* **45**, 157-168, 1997.

© 1996-9

1999-05-26