#! /usr/bin/env python
"""
 This program creates a polar plot of Fay's function, which is also know as 
 a butterfly curve:
        r = e^sin(theta) - 2cos(4theta) + sin(theta/12)^5

 Paul Eugenio
 Florida State University
 PHZ4151C
  29 Jan 2019
"""
from __future__ import division, print_function

import matplotlib.pyplot as plt
import numpy as np

# use latex rendering in lables 
plt.rc('text', usetex=True)

# define parameters
thetaMin, thetaMax = 0, 24*np.pi
steps = 10000


# Using the numpy vectorization
# to generate plot data
theta = np.linspace(thetaMin, thetaMax, steps)
r = np.exp(np.sin(theta)) - 2*np.cos(4*theta)+ np.sin(theta/12)**5
x = r*np.cos(theta)
y = r*np.sin(theta)


# plot curve and decorate with latex equation
plt.plot(x,y)
plt.xlabel(r"$r cos(\theta)$")
plt.ylabel(r"$r sin(\theta)$")
plt.legend([r"$r = e^{sin(\theta)} - 2 cos(4\theta) + sin^5(\theta / {12})$"])
plt.title("Fay's function")
plt.savefig("fay.png")
plt.show()