Interesting Esoterica

Fractal Sequences

Web page by Clark Kimberling
  • Published in 1999
  • Added on
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.)

Links


BibTeX entry

@online{FractalSequences,
	title = {Fractal Sequences},
	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.)},
	url = {https://faculty.evansville.edu/ck6/integer/fractals.html},
	year = 1999,
	author = {Clark Kimberling},
	comment = {},
	urldate = {2019-08-21},
	collections = {easily-explained,fun-maths-facts,integerology,puzzles}
}