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Why does selection sort have quadratic time complexity?

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A three-dimensional Lorenz attractor graph with swirling blue lines forming a butterfly-shaped pattern, representing chaotic motion in a mathematical weather model, with labeled x, y, and z axes. — complexity The weather model of meteorologist Edward Lorenz
The x-, y-, and z-axes correspond to components of the weather, while the graph indicates feasible weather patterns. The graph is a function of time, which means, in theory, that tracing the curve in one direction reveals past weather patterns, while tracing the curve in the other direction predicts future weather patterns. However, practically indistinguishable points may lead to completely different weather epochs, indicated by the two distinct “lobes.” This phenomenon, known as sensitivity to initial conditions, is what prevents precise weather forecasts more than a few days into the future.

Selection sort has quadratic time complexity, denoted as $O (n^{2})$ , because of the way it processes data to order a list. In this sorting algorithm, the procedure requires a pass through the list for every element present. During each of these passes, the algorithm must evaluate every remaining unsorted element to identify the minimum value.1

Because the number of operations required to find the minimum value grows in proportion to the length of the list ( $n$ ), and the number of elements that must be processed also grows with $n$ , the total number of operations scales with the square of the input size. Consequently, the time required to complete the sort increases quadratically as the list grows, making it significantly less efficient than algorithms with lower time complexity, such as those operating in $O (n \log n)$ time.21