How to plot multiple parametric plots in a single figure?

Question

I need to plot a family of parametric curves in a single figure for each alpha values as mentioned in the code

import numpy as np
from sympy import *  
from sympy.plotting import plot_parametric
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


a=45
t = symbols('t')
for alpha in np.arange(0.5,3,.1):
    M=a*sqrt(cos(2*t)+sqrt(pow(alpha,4)+pow(sin(2*t),2)))
    x = M*cos(t)
    y = M*sin(t)
    plot_parametric(x, y, (t, 0, 2*pi))

The code returns a sequence of 2D plots for each alpha value. Instead, I want to plot the whole set of plots in one figure, something like this image attached

Any solution?

Answer 1

from numpy import arange, cos, linspace, pi, sin, sqrt
from matplotlib.pyplot import colorbar, Normalize, show, subplots
from matplotlib.cm import ScalarMappable, viridis

a=45
t= linspace(0, 2*pi, 2001)

norm = Normalize(vmin=0.5, vmax=3)
cmap = viridis
sm = ScalarMappable(cmap=cmap, norm=norm)

fig, (ax_xy, ax_tM) = subplots(1, 2, figsize=(10, 4), constrained_layout=1)

for alpha in arange(0.5,3,.1):
    color = cmap(norm(alpha))
    M=a*sqrt(cos(2*t)+sqrt(pow(alpha,4)+pow(sin(2*t),2)))
    x = M*cos(t)
    y = M*sin(t)
    ax_tM.plot(t, M, color=color)
    ax_xy.plot(x, y, color=color)
colorbar(sm, aspect=40)
show()