Lorenz attractor

lorenz.py

""" Lorenz attractor 

    From https://en.wikipedia.org/wiki/Lorenz_system
    Modified for Sagemath by PM 2Ring 2023.01.04
"""

import numpy as np
from scipy.integrate import odeint

# Build Bezier curves
def bez(pos, tgt):
    pos_tgt = zip(pos, tgt)
    p0, t0 = next(pos_tgt)
    row = [p0]
    curves = []
    for p, t in pos_tgt:
        s = abs(p - p0) / 3
        row.extend([p0 + t0*s, p - t*s, p])
        curves.append(row)
        row = []
        p0, t0 = p, t
    return curves

@interact
def _(rho=28, sigma=10, beta=8/3, hi=40, step=1/10, frame=True, 
  dark=True, color='skyblue', thickness=1, auto_update=False):
    theme = 'dark' if dark else 'light'

    def f(state, t):
        x, y, z = state
        # Derivatives
        return vector([sigma * (y - x), x * (rho - z) - y, x * y - beta * z]) 
    
    state0 = [1.0, 1.0, 1.0]
    times = np.arange(0.0, hi, step)
    
    states = odeint(f, state0, times)

    states = list(map(vector, states))
    grads = [f(state, t).normalized() 
      for state, t in zip(states, times)]
    
    P = bezier3d(bez(states, grads), color=color, thickness=thickness)
    P.show(frame=frame, theme=theme, projection='orthographic')

Here's a live demo running in SageMathCell.