# Logistic Map

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Been playing around with some of the math functions in Python. I think it’s really cool how such a simple formula can create something so complicated. If you’re interested, I’ve documented the code I used to make the video (apologies for the lack of syntax highlighting at the moment):

import numpy as np

from matplotlib import pyplot as plt

from matplotlib import animation

# Set up the figure, the axis, and the plot element

fig = plt.figure()

ax = plt.axes(xlim=(0, 60), ylim=(0, 1))

line, = ax.plot([], [], lw=1)

# initialization function: plot the background of each frame

def init():

line.set_data([], [])

return line,

# animation function. This is called sequentially

def animate(r):

n = np.arange(0,60,1)

x_n = .5 #initial value for x

x_list = [] #initiate list

for i in n:

if i == 0:

x_list.append(x_n) #initial value for x

else:

x_n1 = r*x_n*(1-x_n) #logisitic equation (the magic)

x_list.append(x_n1) #add to x

x_n = x_n1 #new x becomes old x

x = np.array(x_list) #turn list into numpy array

line.set_data(n, x)

return line,

# specify array of parameter values

r = np.arange(2,4.5,.01)

# animate, save, show plot

anim = animation.FuncAnimation(fig, animate, init_func=init,

frames=r, interval=60, blit=True)

#anim.save(‘log_map2.mp4’) #use default ffmpeg

plt.show()