``````

In [1]:

#P165 of "Doing Math with Python": Interactive version of drawing the Barnsley Fern

%matplotlib inline

from ipywidgets import interact
import ipywidgets as widgets

import random
import matplotlib.pyplot as plt

def transformation_1(p):
x = p[0]
y = p[1]
x1 = 0.85*x + 0.04*y
y1 = -0.04*x + 0.85*y + 1.6
return x1, y1

def transformation_2(p):
x = p[0]
y = p[1]
x1 = 0.2*x - 0.26*y
y1 = 0.23*x + 0.22*y + 1.6
return x1, y1

def transformation_3(p):
x = p[0]
y = p[1]
x1 = -0.15*x + 0.28*y
y1 = 0.26*x  + 0.24*y + 0.44
return x1, y1

def transformation_4(p):
x = p[0]
y = p[1]
x1 = 0
y1 = 0.16*y
return x1, y1

def get_index(probability):
r = random.random()
c_probability = 0
sum_probability = []
for p in probability:
c_probability += p
sum_probability.append(c_probability)
for item, sp in enumerate(sum_probability):
if r <= sp:
return item
return len(probability)-1

def transform(p):
# list of transformation functions
transformations = [transformation_1, transformation_2,
transformation_3, transformation_4]
probability = [0.85, 0.07, 0.07, 0.01]
# pick a random transformation function and call it
tindex = get_index(probability)
t = transformations[tindex]
x, y = t(p)
return x, y

def draw_fern(n):
x = [0]
y = [0]
x1, y1 = 0, 0
for i in range(n):
x1, y1 = transform((x1, y1))
x.append(x1)
y.append(y1)

# Plot the points
plt.plot(x, y, 'o')
plt.title('Fern with {0} points'.format(n))
plt.show()

# Allow interaction via the interact() function and an Integer slider widget
i = interact(draw_fern, n=widgets.IntSlider(min=0, max=10000,step=1,value=10))

``````
``````

``````
``````

In [ ]:

``````