Tori spectra

torus_spectra.py

# -*- coding: utf-8 -*-
"""
Based on

https://www.instagram.com/reel/DJpQwikz9Yh/


    [-i 0 t1  0  0 t2]
    [ 0 0  x  x  0  x]
A = [ i 0  0  x  0  i]
    [ 0 0  0 -i -i  i]
    [-i x  0  0 -i  x]
    [-i x  0  0  0 -i]

@author: Nicolás Guarín-Zapata
@date: May 2025
"""
import os
import numpy as np
import matplotlib.pyplot as plt
from scipy.linalg import eigvals
from PIL import Image


def save_gif_PIL(outfile, files, fps=5, loop=0):
    """Helper function for saving GIFs
    
    Parameters
    ----------
    outfile : string
        Path to the output file.
    files : list
        List of paths with the PNG files.
    fps : int (optional)
        Frames per second.
    loop : int
        The number of times the GIF should loop.
        0 means that it will loop forever.
    """
    imgs = [Image.open(file) for file in files]
    imgs[0].save(fp=outfile, format='GIF', append_images=imgs[1:],
                 save_all=True, duration=int(1000/fps), loop=loop)


#%% Image generation
repo = "https://raw.githubusercontent.com/nicoguaro/matplotlib_styles/master"
style = repo + "/styles/neon.mplstyle"
plt.style.use(style)

col1 = "#04D9D9"


npts = 101
niter = 20
files = []
plt.figure(figsize=(4, 4))

for cont, x in enumerate(np.linspace(0, 2, niter)):
    for θ1 in np.linspace(0, 2*np.pi, npts):
        for θ2 in np.linspace(0, 2*np.pi, npts):
            t1 = np.exp(1j*θ1)
            t2 = np.exp(1j*θ2)
            A = np.array([
                [-1j, 0, t1, 0, 0, t2],
                [0, 0, x, x, 0, x],
                [1j, 0, 0, x, 0, 1j],
                [0, 0, 0, -1j, -1j, 1j],
                [-1j, x, 0, 0, -1j, x],
                [-1j, x, 0, 0, 0, -1j]], dtype=complex)
            evals = eigvals(A)
            plt.plot(evals.real, evals.imag, ".", mfc=col1, mec="None",
                     markersize=2, alpha=0.5)

    plt.axis("off")
    file = f"torus_spectra{str(cont).zfill(2)}.png"
    plt.savefig(file, dpi=600)
    files.append(file)
    plt.cla()
    
    
#%% Animation
save_gif_PIL("torus_spectra_anim.gif", files, fps=5, loop=0)

[os.remove(file) for file in files]

torus_spectra_anim.gif