Wrapping all calculations into a function

We will have a look at several implementations to calculate views of the Mandelbrot Set.

To support this some sort of api is helpful, abstracting the base calling convention and defining the necessary bits.

It looks like this.

Show code cell content Hide code cell content

%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 mandelbrot_set(x_min, x_max, y_min, y_max, max_iterations, resolution):
    
    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

    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)
    
    return iterations

tic = time.perf_counter()

iterations = mandelbrot_set(x_min, x_max, y_min, y_max, max_iterations, resolution)

toc = time.perf_counter()
print(f"Calculating the mandelbrot set took {toc-tic:.1f} seconds.")

Calculating the mandelbrot set took 3.2 seconds.

Show code cell content Hide code cell content

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