I think that the constant function could be construed as "self-similar", but also boring. At 12:32 PM 5/28/03 -0700, Eugene Salamin wrote:

--- lkmitch@att.net wrote:

...

... And the signature begins: 1, 2, 1, 3, 2, 4, 1, 3, 5. If you strike the first occurence of every integer in the sequence, you get the original sequence back, which makes this a fractal sequence. ...

What is a fractal sequence? The sequence 1,1,1,1,... also possesses the above mentioned property, but would not reasonably be called fractal.