Mandelbrot Set of Complex Numbers: Visualization¶

Example Image:

Example Image

In [9]:
import numpy as np
import matplotlib.pyplot as plt

Mandelbrot Equation:

In [58]:
#Calculate the finite set of numbers
def mandelbrot(Re, Im, maxIter):
    c = complex(Re, Im)
    z = 0.0j
    
    for i in range(maxIter):
        z = z*z + c
        if(z.real*z.real + z.imag*z.imag) >= 4:
            return i
        
    return maxIter

Convert to image

In [57]:
#Using matplotlb to plot the number set
columns = 700
rows = 700

result = np.zeros([rows, columns])
for row_index, Re in enumerate(np.linspace(-2, 1, num=rows)):
    for column_index, Im in enumerate(np.linspace(-1, 1, num=columns)):
        result[row_index, column_index] = mandelbrot(Re, Im, 100)
        
plt.figure(dpi=100)
plt.imshow(result.T, cmap='twilight_shifted', interpolation='bilinear', extent=[-2, 1, -1, 1])
plt.xlabel("Re")
plt.ylabel("Im")
plt.show()