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
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.