Logistic Map (2021.01)
===

###### tags: `Side Project`, `Python`

## Brief

## Result



## Code

import numpy as np
import matplotlib.pyplot as plt
from numpy.linalg import norm
from matplotlib import style
import math

def logistic(x,mu):
	y = mu*x*(1.0-x)
	return y 

# fill an array with iteration n1 to n2 of the logistic map starting with x0
# and with parameter mu
def fillit(n1,n2,x0,mu):
	x = x0  # initial x value
	z = np.linspace(0.0,1.0,n2-n1)  # create an array
	for i in range(0,n1):   # do n1 iterations
		x = logistic(x,mu)

	for i in range(0,n2-n1):   # fill n2-n1 iterations
		x = logistic(x,mu)
		z[i] = x

	return z

def cal(res):
	k=[]
	for i in range(len(res)):
		a = int(res[i]*1000)
		if (i == 0):
			k.append(a)
		else:
			count = 0
			for j in range(len(k)):
				if(k[j] != a):
					count = count + 0
				else:
					count = count + 1
					break
			if(count == 0):
				k.append(a)
	return (len(k))

# plot the iterated logistic map for nmu number of mu values
def mkplot(mu_min,nmu):  # nmu is number of mu values to use, mu_min range 
	mu_max = 3.6  # maximum mu value
	muarr = np.linspace(mu_min,mu_max,nmu)  
	n1=100  #specify iteration range
	n2=200  
	x0=0.5  # initial x

	for i in range(nmu-1, 0, -1):  
		mu = muarr[i]

		y=fillit(n1,n2,x0,mu)  # get the array of iterations


		test = cal(y)

###############################
		# 收斂成2
		# if(test==2):
		# 	print(test)
		# 	print(y)
		# 	print(i)
		# 	print("mu = " + str(mu))
		# 	break


		# 收斂成1
		# if(test==1):
		# 	print(test)
		# 	print(y)
		# 	print(i)
		# 	print("mu = " + str(mu))
		# 	break

###############################

		x=y*0.0 + mu 
		plt.plot(x,y,',k',markersize=1)



plt.figure()
plt.xlabel(r'$\mu$')
mu_min=2
plt.axis([mu_min, 3.6, 0, 1.0])
mkplot(mu_min,1000)
plt.show()