曼德博集合是一个复数集合,在计算过程中通常需要使用复数对象。不过,如果你想避免使用复数对象,可以通过使用两个浮点数来表示复数的实部和虚部,然后手动进行复数运算。下面是一个使用浮点数进行曼德博集合计算的示例代码:
import numpy as np
import matplotlib.pyplot as plt
def mandelbrot(width, height, real_min, real_max, imag_min, imag_max, max_iter):
real_range = np.linspace(real_min, real_max, width)
imag_range = np.linspace(imag_min, imag_max, height)
pixels = np.empty((width, height))
for x in range(width):
for y in range(height):
c_real = real_range[x]
c_imag = imag_range[y]
z_real = 0.0
z_imag = 0.0
iteration = 0
while iteration < max_iter:
z_real_next = z_real * z_real - z_imag * z_imag + c_real
z_imag_next = 2.0 * z_real * z_imag + c_imag
z_real = z_real_next
z_imag = z_imag_next
if z_real * z_real + z_imag * z_imag > 4.0:
break
iteration += 1
pixels[x, y] = iteration
return pixels
width = 800
height = 600
real_min = -2.0
real_max = 1.0
imag_min = -1.5
imag_max = 1.5
max_iter = 1000
pixels = mandelbrot(width, height, real_min, real_max, imag_min, imag_max, max_iter)
plt.imshow(pixels.T, cmap='hot', extent=(real_min, real_max, imag_min, imag_max))
plt.xlabel('Real')
plt.ylabel('Imaginary')
plt.title('Mandelbrot Set')
plt.show()
这段代码使用了numpy库来处理像素数组,并使用matplotlib库来绘制曼德博集合的图像。使用浮点数进行复数运算可能会导致精度损失,所以你可能会注意到图像的细节不如使用复数对象计算的精确。如果需要更高的精度,你可以考虑使用Python中的decimal模块来进行浮点数运算。