In [1]:
%matplotlib inline
In [2]:
#P151: Drawing a Circle
'''
Example of using matplotlib's Circle patch
'''
import matplotlib.pyplot as plt
def create_circle():
circle = plt.Circle((0, 0), radius = 0.5)
return circle
def show_shape(patch):
ax = plt.gca()
ax.add_patch(patch)
plt.axis('scaled')
plt.show()
if __name__ == '__main__':
c = create_circle()
show_shape(c)
In [5]:
#P153: A growing circle
'''
The animation is not viiewable in notebook. See:
http://jakevdp.github.io/blog/2013/05/12/embedding-matplotlib-animations/
A growing circle
'''
from matplotlib import pyplot as plt
from matplotlib import animation
def create_circle():
circle = plt.Circle((0, 0), 0.05)
return circle
def update_radius(i, circle):
circle.radius = i*0.5
return circle,
def create_animation():
fig = plt.gcf()
ax = plt.axes(xlim=(-10, 10), ylim=(-10, 10))
ax.set_aspect('equal')
circle = create_circle()
ax.add_patch(circle)
anim = animation.FuncAnimation(fig, update_radius, fargs = (circle,), frames=30, interval=50)
plt.title('Simple Circle Animation')
plt.show()
if __name__ == '__main__':
create_animation()
In [6]:
#P156: Animating a projectile's projectory
'''
Animate the trajectory of an object in projectile motion
'''
from matplotlib import pyplot as plt
from matplotlib import animation
import math
g = 9.8
def get_intervals(u, theta):
t_flight = 2*u*math.sin(theta)/g
intervals = []
start = 0
interval = 0.005
while start < t_flight:
intervals.append(start)
start = start + interval
return intervals
def update_position(i, circle, intervals, u, theta):
t = intervals[i]
x = u*math.cos(theta)*t
y = u*math.sin(theta)*t - 0.5*g*t*t
circle.center = x, y
return circle,
def create_animation(u, theta):
intervals = get_intervals(u, theta)
xmin = 0
xmax = u*math.cos(theta)*intervals[-1]
ymin = 0
t_max = u*math.sin(theta)/g
ymax = u*math.sin(theta)*t_max - 0.5*g*t_max**2
fig = plt.gcf()
ax = plt.axes(xlim=(xmin, xmax), ylim=(ymin, ymax))
circle = plt.Circle((xmin, ymin), 1.0)
ax.add_patch(circle)
anim = animation.FuncAnimation(fig, update_position,
fargs=(circle, intervals, u, theta),
frames=len(intervals), interval=1,
repeat=False)
plt.title('Projectile Motion')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
if __name__ == '__main__':
try:
u = float(input('Enter the initial velocity (m/s): '))
theta = float(input('Enter the angle of projection (degrees): '))
except ValueError:
print('You entered an invalid input')
else:
theta = math.radians(theta)
create_animation(u, theta)
In [7]:
#P160: Random walk of a point in a plane
'''
Example of selecting a transformation from two equally probable
transformations
'''
import matplotlib.pyplot as plt
import random
def transformation_1(p):
x = p[0]
y = p[1]
return x + 1, y - 1
def transformation_2(p):
x = p[0]
y = p[1]
return x + 1, y + 1
def transform(p):
# list of transformation functions
transformations = [transformation_1, transformation_2]
# pick a random transformation function and call it
t = random.choice(transformations)
x, y = t(p)
return x, y
def build_trajectory(p, n):
x = [p[0]]
y = [p[1]]
for i in range(n):
p = transform(p)
x.append(p[0])
y.append(p[1])
return x, y
if __name__ == '__main__':
# initial point
p = (1, 1)
n = int(input('Enter the number of iterations: '))
x, y = build_trajectory(p, n)
# plot
plt.plot(x, y)
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
In [8]:
#P165: Draw Barnsley Fern
'''
Draw Barnsley Fern
'''
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):
# We start with (0, 0)
x = [0]
y = [0]
x1, y1 = 0, 0
for i in range(n):
x1, y1 = transform((x1, y1))
x.append(x1)
y.append(y1)
return x, y
if __name__ == '__main__':
n = int(input('Enter the number of points in the Fern: '))
x, y = draw_fern(n)
# Plot the points
plt.plot(x, y, 'o')
plt.title('Fern with {0} points'.format(n))
plt.show()
In [16]:
#P174: Example of using the imshow() function
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import random
def initialize_image(x_p, y_p):
image = []
for i in range(y_p):
x_colors = []
for j in range(x_p):
x_colors.append(0)
image.append(x_colors)
return image
def color_points():
x_p = 20
y_p = 20
image = initialize_image(x_p, y_p)
for i in range(y_p):
for j in range(x_p):
image[i][j] = random.randint(0, 10)
plt.imshow(image, origin='lower', extent=(0, 5, 0, 5),
cmap=cm.Greys_r, interpolation='nearest')
plt.colorbar()
plt.show()
if __name__ == '__main__':
color_points()