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R10592/BOX COUNTING/BoxHenonMap.py
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BoxHenonMap.py
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from matplotlib import pyplot as plt
import numpy as num
import math
import time
import numpy as num
import matplotlib.pyplot as plt
#The code calculate the number of boxes intersected for chosen scaling factors for the henon map (2D)
m=10000; #nr of points calculated
a=1.4; #Parameters of Henon map
b=0.3;
#calculate points of Henon map
x=num.zeros(m);
y=num.zeros(m);
for i in range(m-1):
x[i+1]=1-a*x[i]**2+y[i]
y[i+1]=b*x[i]
#Min and Max coordinates of Henon map to find the first box
XBoxmin=2*min(min(x), min(y));
XBoxmax=2*max(max(x), max(y));
#1.0000001
print(XBoxmin)
print(XBoxmax)
#Length of the first box
LBox = XBoxmax - XBoxmin;
print(LBox)
steps=15; #Number of steps for the computation
#sf=num.zeros(steps); #scaling factors
sf=[5,7,10,15,20,25,30,40,50,60,70,80,100,120,150];
NBox=num.zeros(steps,dtype=int); #nr of total boxes for each scaling factor
for i in range(steps):
#sf[i]=2**(i+1);
NBox[i]=int(sf[i]**3);
print('scaling factors:')
print(sf)
print('Nr. of total boxes:')
print(NBox)
NN=num.zeros(steps,dtype=int); #nr. of intersected boxes
t = time.time()
#Non optimized box counting
for i in range(steps):
lbox=LBox/sf[i] #length of boxes
print(sf[i]) #to check the advancement
for j in range(int(sf[i])):
for k in range(int(sf[i])):
for n in range(m):
if x[n] >= XBoxmin + k * lbox and x[n] <= XBoxmin + (k + 1) * lbox and y[n] >= XBoxmin + j * lbox and y[n] <= XBoxmin + (j + 1) * lbox:
NN[i] = NN[i] + 1
break
elapsed = time.time() - t
print('Nr. of intersected boxes')
print(NN)
#plot Henon map and Min. Max. coordinates of the first obx
fig, ax = plt.subplots(1, 1)
plt.scatter(x, y, s=0.7, label='points of the classical Hénon Map')
ax.set(xlabel='x', ylabel='y')
ax.grid()
plt.legend(loc="lower right")
plt.show()
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