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.
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.