# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as pl
import time
import pylab as pl
from matplotlib import cm
def shuye():
# 蕨类植物叶子的迭代函数和其概率值
eq1 = np.array([[0,0,0],[0,0.16,0]])
p1 = 0.01
eq2 = np.array([[0.2,-0.26,0],[0.23,0.22,1.6]])
p2 = 0.07
eq3 = np.array([[-0.15, 0.28, 0],[0.26,0.24,0.44]])
p3 = 0.07
eq4 = np.array([[0.85, 0.04, 0],[-0.04, 0.85, 1.6]])
p4 = 0.85
def ifs(p, eq, init, n):
# 迭代向量的初始化
pos = np.ones(3, dtype=np.float)
pos[:2] = init
# 通过函数概率,计算函数的选择序列
p = np.add.accumulate(p)
rands = np.random.rand(n)
select = np.ones(n, dtype=np.int)*(n-1)
for i, x in enumerate(p[::-1]):
select[rands<x] = len(p)-i-1
# 结果的初始化
result = np.zeros((n,2), dtype=np.float)
c = np.zeros(n, dtype=np.float)
for i in range(n):
eqidx = select[i] # 所选的函数下标
tmp = np.dot(eq[eqidx], pos) # 进行迭代
pos[:2] = tmp # 更新迭代向量
# 保存结果
result[i] = tmp
c[i] = eqidx
return result[:,0], result[:, 1], c
start = time.clock()
x, y, c = ifs([p1,p2,p3,p4],[eq1,eq2,eq3,eq4], [0,0], 100000)
print(time.clock() - start)
pl.figure(figsize=(6,6))
pl.subplot(121)
pl.scatter(x, y, s=1, c="g", marker="s", linewidths=0)
pl.axis("equal")
pl.axis("off")
pl.subplot(122)
pl.scatter(x, y, s=1,c = c, marker="s", linewidths=0)
pl.axis("equal")
pl.axis("off")
pl.subplots_adjust(left=0,right=1,bottom=0,top=1,wspace=0,hspace=0)
pl.gcf().patch.set_facecolor("white")
pl.show()
def mandelbrot():
def iter_point(c):
z = c
for i in range(1, 100): # 最多迭代100次
if abs(z)>2: break # 半径大于2则认为逃逸
z = z*z+c
return i # 返回迭代次数
def draw_mandelbrot(cx, cy, d):
x0, x1, y0, y1 = cx-d, cx+d, cy-d, cy+d
y, x = np.ogrid[y0:y1:200j, x0:x1:200j]
c = x + y*1j
start = time.clock()
mandelbrot = np.frompyfunc(iter_point,1,1)(c).astype(np.float)
print("time=",time.clock() - start)
pl.imshow(mandelbrot, cmap=cm.Blues_r, extent=[x0,x1,y0,y1])
pl.gca().set_axis_off()
x,y = 0.27322626, 0.595153338
pl.subplot(231)
draw_mandelbrot(-0.5,0,1.5)
for i in range(2,7):
pl.subplot(230+i)
draw_mandelbrot(x, y, 0.2**(i-1))
pl.subplots_adjust(0.02, 0, 0.98, 1, 0.02, 0)
pl.show()
if __name__ == '__main__':
mandelbrot()