CODEWITHSUNDEEP
pythonnumpymandelbrot
krolik2002
krolik2002

Reputation: 53

Zooming in on Mandelbrot set

I have the following code:


# MANDELBROT

a = np.arange(-2, 2, 0.01)
b = np.arange(-2, 2, 0.01)
M_new = new_matrix(a, b)
plt.imshow(M_new, cmap='gray', extent=(-2, 2, -2, 2))
plt.show()

## ZOOMING

a_2 = np.arange(0.1, 0.5, 0.01)
b_2 = np.arange(0.1, 0.5, 0.01)
M_new_2 = new_matrix(a_2, b_2)
plt.imshow(M_new_2, cmap='gray', extent=(0.1, 0.5, 0.1, 0.5))
plt.show()

When I plot the Mandelbrot it looks fine, but what I want to do next is to zoom in on specific part of the set (between 0,1 - 0,5 both x and y-axis). I do not know if the second part of the code is incorrect or maybe I am thinking in a wrong way.

Upvotes: 0

Views: 2212

Answers (2)

Mark Tolonen
Mark Tolonen

Reputation: 177755

Make sure to generate the array size you want (401x401) and plot those points correctly in the matrix. As you zoom in you don't want .01 increments between your extents, but exactly 401 steps. Use np.linspace for that. Also making a common function for showing the matrix helps make the math consistent:

import numpy as np
from matplotlib import pyplot as plt

SIZE = 401

def mandelbrot(c: complex):
    z = complex(0, 0)
    for i in range(100):
        z = z*z+c
    return np.abs(z) <= 2

def new_matrix(a_1, b_1):
    M = np.zeros(SIZE*SIZE).reshape(SIZE, SIZE)
    for i,number1 in enumerate(a_1):
        for j,number2 in enumerate(b_1):
            M[i,j] = mandelbrot(complex(number1, number2))
    return M

def show(x1,y1,x2,y2):
    a = np.linspace(x1, y1, SIZE)
    b = np.linspace(x2, y2, SIZE)
    M = new_matrix(a, b)
    plt.imshow(M, cmap='gray', extent=(x1, y1, x2, y2))
    plt.show()

show(-2,2,-2,2)
show(.1,.5,.1,.5)

Output:

enter image description here

enter image description here

Upvotes: 2

Dr. V
Dr. V

Reputation: 1914

I did several changes to you code, mainly respecting the shape of the input arrays.

import numpy as np
from matplotlib import pyplot as plt

def mandelbrot(c: complex):
    m = 0
    z = complex(0, 0)
    for i in range(0, 100):
        z = z*z+c
        m += 1
        if np.abs(z) > 2:
            return False
    return True

def new_matrix(a_1, b_1):
    M = np.zeros((a_1.shape[0], b_1.shape[0]))
    for i, number1 in enumerate(a_1):
        for j, number2 in enumerate(b_1):
            M[i, j] = mandelbrot(complex(number1, number2))
    return M

# MANDELBROT

a = np.arange(-2, 2, 0.01)
b = np.arange(-2, 2, 0.01)

M_new = new_matrix(a, b)

plt.imshow(M_new, cmap='gray', extent=(-2, 2, -2, 2))
plt.show()

## ZOOMING

a_2 = np.arange(0.1, 0.5, 0.01)
b_2 = np.arange(0.1, 0.5, 0.01)

M_new_2 = new_matrix(a_2, b_2)
plt.imshow(M_new_2, cmap='gray', extent=(0.1, 0.5, 0.1, 0.5))
plt.show()

Check in particular the definition of the matrix M (using the shape of the input arguments, and the enumerate construct in the for loops.

It could without doubt be optimized further, but at least this makes it working. You might want to use linspace in your application, to have better control over the number of points generated.

Upvotes: 1

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