# Fractal Sequences

• Published in 1999
In the collections
Fractal sequences have in common with the more familiar geometric fractals the property of self-containment. An example of a fractal sequence is 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, . . . If you delete the first occurrence of each positive integer, you'll see that the remaining sequence is the same as the original. (So, if you do it again and again, you always get the same sequence.)

## Other information

key
FractalSequences
type
online
2019-08-21
date_published
1999-09-14

### BibTeX entry

@online{FractalSequences,
key = {FractalSequences},
type = {online},
title = {Fractal Sequences},
author = {Clark Kimberling},
abstract = { Fractal sequences have in common with the more familiar geometric fractals the property of self-containment. An example of a fractal sequence is

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, . . .

If you delete the first occurrence of each positive integer, you'll see that the remaining sequence is the same as the original. (So, if you do it again and again, you always get the same sequence.)},
comment = {},
}