What is it called when a decimal value has a pattern while infinite? 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.
 A: There's no real term for it.
It's an irrational number though.
We refer to "patterns" but what we really mean and are interested in is "periodic".  For a periodic decimal, there is a point where every $k$th decimal term repeats; that is to say, for large enough $j$ then the $j$th decimal, $a_j$, will be equal to the $j+k$the decimal, $a_{j+k} = a_j$.
The only reason we are interest in that type of pattern is because that means the value itself is rational. 
All numbers are either rational, can be written as $\frac mn$ where $m$ and $n$ are integers.  Tho write the decimal of $\frac mn$ there are only so many possible remainders so we must repeat remainders eventually. That leads to an infinite loop with a periodic repeating.  Likewise if we have a periodic repeat of period $k$ and we multiply by $10^k - 1$ we get something that terminates so it must be rational.
So we have the very useful result: An number is rational if and only if it's decimal expansion is periodic.  
Or to make the language to high school students simpler and not intimidating: "if the decimal has a pattern".
So the pattern you describe is ... interesting and probably be worth studying.  But algebraically it doesn't have any significance, in and of itself.
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Post-script:  It's important to realize "decimal numbers that repeat periodically are rational" is a consequence; not a definition. (They are ratios of integers and the periodic repeating is just a consequence.)  Here "incremental patterns" are number with predictable patterns such as $.101001000100001000001.....$ are a definition itself.
