I recently made an edit to this post concerning $\pi$ and it containing all possible combinations of numerical values; and this answer to it brought forward an interesting number:

0.011000111100000111111…

This got me thinking; what is it called when a number has a pattern that can be replicated infinitely, though the same number never repeats. The best example is the above referenced nuber; when this is broken down:

0, 11, 000, 1111, 00000, 111111

Granted even this is not a perfect example as `zero`

and `one`

are repeated which breaks the *same number never repeats* rule if you take it that far; this would mean that further definition is required.

I suppose a thorough definition would be more of:

A number whose digits represent a pattern that can be scaled infinitely, without repeating grouped digits such as:

10110111 - zero repeats, not a true resemblance.

011000111100000111111 - zeros are grouped, true resemblance.

* The Question at Hand*: what is it called when a number has a pattern that can be replicated infinitely, though the same number never repeats.