迭代公式的指数，使用的1+5j，这是个复数，所以是广义mandelbrot集，大家可以自行修改指数，得到其他图形。各种库安装不全的，自行想办法

Python 3.6.7。

Linux系统：Ubuntu 18.04.2

完整代码：

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<pre spellcheck="false" style="box-sizing: border-box; margin: 5px 0px; padding: 5px 10px; border: 0px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 400; font-stretch: inherit; font-size: 16px; line-height: inherit; font-family: inherit; vertical-align: baseline; cursor: text; counter-reset: list-1 0 list-2 0 list-3 0 list-4 0 list-5 0 list-6 0 list-7 0 list-8 0 list-9 0; background-color: rgb(240, 240, 240); border-radius: 3px; white-space: pre-wrap; color: rgb(34, 34, 34); letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-style: initial; text-decoration-color: initial;">#encoding=utf-8
import numpy as np
import pylab as pl
import time
from matplotlib import cm
from math import log
escape_radius = 10
iter_num = 20
def draw_mandelbrot2(cx, cy, d, N=600):
global mandelbrot
"""
绘制点(cx, cy)附近正负d的范围的Mandelbrot
"""
x0, x1, y0, y1 = cx-d, cx+d, cy-d, cy+d
y, x = np.ogrid[y0:y1:N1j, x0:x1:N1j]
c = x + y1j
smooth_mand = np.frompyfunc(smooth_iter_point,1,1)(c).astype(np.float)
pl.gca().set_axis_off()
pl.imshow(smooth_mand, cmap=cm.Blues_r, extent=[x0,x1,y1,y0])
pl.show()
def smooth_iter_point(c):
z = c #赋初值
d = 1+2j #这里，把幂运算的指数，设定成复数1+2j， 就是广义mandelbrot集合， d=2就是标准mandelbrot集，d=3就是三阶的
for i in range(1, iter_num):
if abs(z)>escape_radius: break
z = zd+c # 运算符是幂运算
#下面是重新计算迭代次数，可以获取连续的迭代次数（即正规化）
absz = abs(z) #复数的模
if absz > 2.0:
mu = i - log(log(abs(z),2),2)
else:
mu = i
return mu # 返回正规化的迭代次数
def draw_mandelbrot(cx, cy, d, N=800):
"""
绘制点(cx, cy)附近正负d的范围的Mandelbrot
"""
global mandelbrot
x0, x1, y0, y1 = cx-d, cx+d, cy-d, cy+d
y, x = np.ogrid[y0:y1:N1j, x0:x1:N1j]
c = x + y1j
# 创建X,Y轴的坐标数组
ix, iy = np.mgrid[0:N,0:N]
# 创建保存mandelbrot图的二维数组，缺省值为最大迭代次数
mandelbrot = np.ones(c.shape, dtype=np.int)*100
# 将数组都变成一维的
ix.shape = -1
iy.shape = -1
c.shape = -1
z = c.copy() # 从c开始迭代，因此开始的迭代次数为1
start = time.clock()
for i in xrange(1,100):
# 进行一次迭代
z *= z
z += c
# 找到所有结果逃逸了的点
tmp = np.abs(z) > 2.0
# 将这些逃逸点的迭代次数赋值给mandelbrot图
mandelbrot[ix[tmp], iy[tmp]] = i
# 找到所有没有逃逸的点
np.logical_not(tmp, tmp)
# 更新ix, iy, c, z只包含没有逃逸的点
ix,iy,c,z = ix[tmp], iy[tmp], c[tmp],z[tmp]
if len(z) == 0: break
print ("time="),time.clock() - start
pl.imshow(mandelbrot, cmap=cm.Blues_r, extent=[x0,x1,y1,y0])
pl.gca().set_axis_off()
pl.show()

鼠标点击触发执行的函数

def on_press(event):
global g_size
print (event)
print (dir(event))
newx = event.xdata
newy = event.ydata
print (newx)
print (newy)
#不合理的鼠标点击，直接返回，不绘制
if newx == None or newy == None or event.dblclick == True:
return None
#不合理的鼠标点击，直接返回，不绘制
if event.button == 1: #button ==1 代表鼠标左键按下， 是放大图像
g_size /= 2
elif event.button == 3: #button == 3 代表鼠标右键按下， 是缩小图像
g_size *= 2
else:
return None
print (g_size)
draw_mandelbrot2(newx,newy,g_size)
fig, ax = pl.subplots(1)
g_size = 2.5

注册鼠标事件

fig.canvas.mpl_connect('button_press_event', on_press)

初始绘制一个图

draw_mandelbrot2(0,0,g_size)
</pre>

效果图如下：

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<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1) 0s;"></tt-image>