Wrapping the core calculation into a function

Now its about time to start speeding up things.

The first idea here might be to just prepare that by cleaning up the code a bit and bring more structure to it.

We have the outer two loops to iterate the complex grid and the innermost for loop to execute the actual algorithm.

So let’s start off with wrapping the core algorithm in its own function.

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%matplotlib widget
import time
import matplotlib.pyplot as plt
plt.rcParams['figure.dpi'] = 300

x_min, x_max = -2.5, 1.0
y_min, y_max = -1.25, 1.25
max_iterations = 100
resolution = 1000

def mandel(x, y, max_iterations):
    c = complex(x, y)
    c0 = c
    
    for iteration in range(max_iterations):
        c = c**2 + c0
        if abs(c) > 2.0:
            break
    
    return iteration

tic = time.perf_counter()

x = [x_min + (x_max - x_min) / (resolution - 1) * index for index in range(resolution)]
y = [y_min + (y_max - y_min) / (resolution - 1) * index for index in range(resolution)]

iterations = []
for _y in y:
    row = []
    for _x in x:
        row.append(mandel(_x, _y, max_iterations))
        
    iterations.append(row)
    
toc = time.perf_counter()
print(f"Calculating the mandelbrot set took {toc-tic:.1f} seconds.")

Calculating the mandelbrot set took 3.6 seconds.

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fig, axes = plt.subplots()
axes.imshow(iterations[::-1], extent=(x_min, x_max, y_min, y_max), cmap="RdGy")
plt.tight_layout()

This already gave a permance win.

But why?