Coding Example: The Mandelbrot Set (NumPy approach)
Understand how to implement the Mandelbrot set using NumPy vectorization to enhance computational efficiency. Explore multiple NumPy-based solutions, benchmark their performance against traditional Python code, and learn visualization techniques to display results with improved detail and fewer artifacts.
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Solution 1: NumPy Implementation
The trick is to search at each iteration values that have not yet diverged and update relevant information for these values and only these values. Because we start from Z = 0, we know that each value will be updated at least once (when they’re equal to 0, they have not yet diverged) and will stop being updated as soon as they’ve diverged. To do that, we’ll use NumPy fancy indexing with the less(x1,x2) function that return the truth value of (x1 ...