The problem involves calculating the total length of a curve generated through an iterative process. Let's examine how the iterative process affects the length:

Explanation:

Given the figures, it seems that in each iteration, the line segments are divided and modified. This resembles a process like creating a Koch snowflake:

1. Initial Condition: At iteration 0, the line is a simple straight line of length 1.
2. Iteration 1: The line is divided into 3 parts. For each segment, the middle third is replaced by two segments of equal length, forming a peak. This transformation makes the length of each segment \(\frac{1}{3}\), and the total number of segments becomes 4 times the original number.
3. Iteration 2: The process repeats on each segment, increasing the total number of segments once again by 4/3 times the previous length.

Deriving the formula:

With each iteration:

• The total number of segments increases by a factor of \(\frac{4}{3}\).
• The length of each individual segment decreases by a factor of \(\frac{1}{3}\).

Thus, the total length after iteration \(n\) can be expressed as:

\[ L_n = (L_0) \times \left( \frac{4}{3} \right)^n \times \left(\frac{1}{3}\right)^n = (L_0) \times \left(\frac{4}{3} \times \frac{1}{3}\right)^n \]

Since the initial length \(L_0 = 1\), the total length after \(n\) iterations is:

\[ L_n = \left(\frac{5}{3}\right)^n \]

Conclusion:

The correct option is \(\left(\frac{5}{3}\right)^n\), which matches the given configuration.