Python体内的巴恩斯利蕨
巴恩斯利蕨是数学家迈克尔·巴恩斯利创造的分形形状。这种分形的几何特征类似天然蕨类植物，因此得名。巴恩斯利蕨是通过对四个数学方程进行大量迭代而产生的，由巴恩斯利引入，被称为迭代函数系统(IFS) 。
巴恩斯利使用的转换公式为:
，其中字母具有以下值:
| 一 | b | c | d | e | f | p | 零件 |
|---|---|---|---|---|---|---|---|
| Zero | Zero | Zero | Zero point one six | Zero | Zero | Zero point zero one | 阻止 |
| Zero point eight five | Zero point zero four | -0.04 | Zero point eight five | Zero | One point six | Zero point eight five | 小传单 |
| Zero point two | -0.26 | Zero point two three | Zero point two two | Zero | One point six | Zero point zero seven | 大传单(左) |
| -0.15 | Zero point two eight | Zero point two six | Zero point two four | Zero | Zero point four four | Zero point zero seven | 大传单(右) |
而“p”是概率。
于是这四个方程是:
借助于上面的方程，蕨类植物就产生了。现在让我们看看 Python3 的实现。
# importing necessary modules
import matplotlib.pyplot as plt
from random import randint
# initializing the list
x = []
y = []
# setting first element to 0
x.append(0)
y.append(0)
current = 0
for i in range(1, 50000):
# generates a random integer between 1 and 100
z = randint(1, 100)
# the x and y coordinates of the equations
# are appended in the lists respectively.
# for the probability 0.01
if z == 1:
x.append(0)
y.append(0.16*(y[current]))
# for the probability 0.85
if z>= 2 and z<= 86:
x.append(0.85*(x[current]) + 0.04*(y[current]))
y.append(-0.04*(x[current]) + 0.85*(y[current])+1.6)
# for the probability 0.07
if z>= 87 and z<= 93:
x.append(0.2*(x[current]) - 0.26*(y[current]))
y.append(0.23*(x[current]) + 0.22*(y[current])+1.6)
# for the probability 0.07
if z>= 94 and z<= 100:
x.append(-0.15*(x[current]) + 0.28*(y[current]))
y.append(0.26*(x[current]) + 0.24*(y[current])+0.44)
current = current + 1
plt.scatter(x, y, s = 0.2, edgecolor ='green')
plt.show()
输出:
注:整个输出取决于方程的系数。一个实验可能是改变系数，每次得到一个新的模式。
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