Visualizing Chebyschev Polynomials

ChebyschevPolynomial.py

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation, PillowWriter

xspace = np.linspace(-1, 1, 500)
thetaspace = np.linspace(np.pi, 0, 500)

centeredthetaspace = np.linspace(-np.pi/2, np.pi/2, 500)

end = [
    np.cos(1 * thetaspace),
    np.cos(2 * thetaspace),
    np.cos(3 * thetaspace),
    np.sqrt(1 - xspace * xspace)
]

start = [
    np.cos(1 * np.arccos(xspace)),
    np.cos(2 * np.arccos(xspace)),
    np.cos(3 * np.arccos(xspace)),
    np.zeros_like(xspace)
]
fig, ax = plt.subplots(figsize=(6, 4), layout="constrained")

ax.axis(False) # disable axis

plots = [
    ax.plot(xspace, start[0], lw=2.25, color="red", alpha=0.8)[0],
    ax.plot(xspace, start[1], lw=2.25, color="red", alpha=0.5)[0],
    ax.plot(xspace, start[2], lw=2.25, color="red", alpha=0.3)[0],
    ax.plot(xspace, start[3], lw=2.25, color="#1F0E9E", alpha=0.4)[0]
]
ax.plot(xspace, np.zeros(500), color="#1F0E9E", lw=2.25)
left = ax.text(-1.05, -0.125, "-1", fontname="Futura", fontsize=8)
right = ax.text(0.98, -0.125, "1", fontname="Futura", fontsize=8)

def frame(frac):
    if frac < 0.5:
        left.set_text("-1")
        right.set_text("1")
    else:
        left.set_text("π")
        right.set_text("0")

    def do_plot(i):
        s = start[i]
        e = end[i]
        y = (s + (e - s) * frac)
        plots[i].set_data(xspace, y)
        
        return plots[i]
    
    
    return [do_plot(i) for i in range(len(plots))]


progress = np.concatenate([np.ones(20), np.linspace(1, 0, 100), np.zeros(20), np.linspace(0, 1, 100)])
FuncAnimation(fig, frame, frames=progress, blit=True).save(
    "chebyschev-polynomial.gif", writer=PillowWriter(fps=30), dpi=200, )