How can I increase the precision of the calculations in this python code

August 6, 2023

I am trying to reproduce a plot on page 81 of Math Letters Jr. (which is a great recreational math book, by the way). The plot is created using a pair of simple functions that are applied iteratively (i.e. the output of each loop is the input for the following loop). Plotting the output x, y point in each loop should produce a beautiful complex point cloud. However, when I implemented the code below, it gets stuck cycling between 4 identical points after the fiftieth iteration. I assume this is due to rounding due to insufficient precision in my variable definitions. How can I improve on this?

import matplotlib.pyplot as plt

x = 0
y = 0
vecx = []
vecy = []

for i in range(5000):
    x = 1.3 + 0.3*x + 0.6*x*y - 0.6*y - y**2
    y = 0.1 - 0.7*x + 0.5*(x**2) - 0.8*x*y + 0.1*y - 0.6*(y**2)
    vecx.append(x)
    vecy.append(y)
    
plt.plot(vecx, vecy, 'b.')

>Solution :

One thing you can do is use the decimal module of Python:

from decimal import Decimal, getcontext

# Set the precision for decimal calculations
getcontext().prec = 50  # You can adjust the precision as needed

x = Decimal('0')
y = Decimal('0')
vecx = []
vecy = []

for i in range(5000):
    x_new = Decimal('1.3') + Decimal('0.3') * x + Decimal('0.6') * x * y - Decimal('0.6') * y - y**2
    y_new = Decimal('0.1') - Decimal('0.7') * x + Decimal('0.5') * (x**2) - Decimal('0.8') * x * y + Decimal('0.1') * y - Decimal('0.6') * (y**2)
    x, y = x_new, y_new
    vecx.append(x)
    vecy.append(y)