import numpy as np import matplotlib.pyplot as plt from scipy.integrate import solve_ivp

def rossler_system(t, xyz, a, b, c):

   x, y, z = xyz
   dx_dt = -y - z
   dy_dt = x + a * y
   dz_dt = b + z * (x - c)
   return [dx_dt, dy_dt, dz_dt]

1. Rossler system parameters

a = 0.2 b = 0.2 c = 5.7

1. Initial conditions

xyz0 = [1.0, 1.0, 1.0] tmin, tmax = 0, 10000 t_span = [tmin, tmax] t_resolution = 100 t_eval = np.linspace(t_span[0], t_span[1], (tmax-tmin) * t_resolution)

solution = solve_ivp(rossler_system, t_span, xyz0, args=(a, b, c), t_eval=t_eval) x, y, z = solution.y

%%capture import os

xmin, xmax = min(x) + (min(x) - max(x))*0.03, max(x) + (max(x) - min(x))*0.03

for i, delay in enumerate(range(1, 601, 5)):

   fig = plt.figure(figsize=(10, 10))
   ax = fig.add_subplot(111)
   ax.plot(x[:-(delay)], x[(delay):], color='k', linewidth=0.04, alpha=0.8)
   ax.axis("off")
   ax.set_xlim(xmin, xmax)
   ax.set_ylim(xmin, xmax)

   title = ax.set_title(f"Rössler attractor reconstructed with delay t={delay/t_resolution:0.2f}", fontsize=20)
   title.set_position((0.1,0))
   title.set_ha('left')
   title.set_va('bottom')

   dir_path = f"./rossler"
   if not os.path.exists(dir_path):
       os.makedirs(dir_path)

   fig.savefig(f"{dir_path}/{i}.png")
   plt.close()

import imageio.v3 as iio import os from natsort import natsorted import moviepy.editor as mp

for dir_path in ["./rossler"]:

   file_names = natsorted((fn for fn in os.listdir(dir_path) if fn.endswith('.png')))

   # Create a list of image files and set the frame rate
   images = []
   fps = 12

   # Iterate over the file names and append the images to the list
   for file_name in file_names:
       file_path = os.path.join(dir_path, file_name)
       images.append(iio.imread(file_path))

   filename = dir_path[2:]
   iio.imwrite(f"{filename}.gif", images, duration=1000/fps, rewind=True)
   clip = mp.ImageSequenceClip(images, fps=fps)
   clip.write_videofile(f"{filename}.mp4")