[Rule 110] is a Turing complete cellular automaton. It is defined as follows:
Take as initial value a sequence of symbols that's infinite to both sides, which consists only of two different symbols (I'm going to use $+$ and $-$ here). This sequence can be seen as a function that maps the integers to the set $\\{+,-\\}$.
Then in each iteration, calculate a new such sequence as follows:
To determine the new value at position $n$, look at the old values in the cells $n-1$, $n$ and $n+1$, and then look up the new value in the following table:
<div>
\begin{align}
\begin{array}{c|cccccccc}
\text{old} & +++ & ++- & +-+ & +-- & -++ & -+- & --+ & ---\\
\hline
\text{new} & - & + & + & - & + & + & + & -
\end{array}
\end{align}
</div>
Your task is to implement Rule 110. In particular, your program shall take as input:
* A non-empty string that represents a pattern which is periodically repeated to both sides, starting at position 0 (so if the string is `+-`, then there's a `+` on all even positions, and a `-` on all odd positions.
* A second (empty or non-empty) string that represents a local deviation from that pattern, again starting at position 0. for example, with the above background pattern, if the second string is `---+++`, then the initial state of the cellular automaton is
```
...+-+-+-+----++++-+-+-...
↑
position 0
```
* A number of iterations, which may be zero or positive.
It then outputs the relevant part resulting state of the state space as string. More exactly, if your pattern has length $p$ your local disturbance has length $l$, and the number of iterations is $n$, then you need to print the output space from position $-2p-n$ up to position $l+2p+n-1$ inclusive.
You may use arbitrary sequence types (such as list or tuples) instead of strings. Also you may use arbitrary characters instead of `+` and `-`, or values of other types (e.g. integers or logical values), as long as you have exactly two of them and state clearly which of them corresponds to $+$ and which to $-$.
This is <span class="badge is-tag">code-golf</span>, thus the shortest code wins.
Test cases:
```
Pattern: "-"
Local: ""
Iterations: 0
----
Output: "----"
Pattern: "-"
Local: "+"
Iterations: 0
----
Output: "--+--"
Pattern: "-"
Local: "-"
Iterations: 0
----
Output: "-----"
Pattern: "+-"
Local: "-"
Iterations: 0
----
Output: "+-+---+-+"
Pattern: "-+"
Local: "-"
Iterations: 0
----
Output: "-+-+-+-+-"
Pattern: "+"
Local: ""
Iterations: 1
----
Output: "------"
Pattern: "+-"
Local: ""
Iterations: 1
----
Output: "++++++++++"
Pattern: "-"
Local: "+"
Iterations: 1
----
Output: "--++---"
Pattern: "-"
Local: "+"
Iterations: 3
----
Output: "--++-+-----"
Pattern: "+---"
Local: ""
Iterations: 3
----
Output: "++-+++-+++-+++-+++-+++"
Pattern: "+-"
Local: "-"
Iterations: 3
----
Output: "----+++++------"
```
**Note:** Please verify the test cases; I've evaluated them by hand, so I might have made a mistake.
[Rule 110]: https://en.wikipedia.org/wiki/Rule_110
