lorenz_2d_dynamic_multiplot.py

# Vykreslení Lorenzova atraktoru s různými parametry s a r

# MIT License
#
# Copyright (c) 2024 Pavel Tišnovský
#
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import matplotlib.pyplot as plt
import numpy as np


def lorenz(x, y, z, s=10, r=28, b=2.667):
    """Výpočet dalšího bodu Lorenzova atraktoru."""
    x_dot = s * (y - x)
    y_dot = r * x - y - x * z
    z_dot = x * y - b * z
    return x_dot, y_dot, z_dot


# krok (změna času)
dt = 0.01

# celkový počet vypočtených bodů na Lorenzově atraktoru
n = 500


def draw_lorenz_for_input_values(ax, dt, n, x0, y0, z0):
    # prozatím prázdné pole připravené pro výpočet
    x = np.zeros((n,))
    y = np.zeros((n,))
    z = np.zeros((n,))

    # počáteční hodnoty
    x[0], y[0], z[0] = (x0, y0, z0)

    # vlastní výpočet atraktoru
    for i in range(n - 1):
        x_dot, y_dot, z_dot = lorenz(x[i], y[i], z[i])
        x[i + 1] = x[i] + x_dot * dt
        y[i + 1] = y[i] + y_dot * dt
        z[i + 1] = z[i] + z_dot * dt

    # vykreslení grafu
    ax.plot(y.copy(), z.copy())


# konstrukce 2D grafu
fig = plt.figure(figsize=(8, 6))

# Vykreslení Lorenzova atraktoru s různými parametry s a r
for yi in range(5):
    for xi in range(5):
        ax = fig.add_subplot(5, 5, xi + 1 + yi * 5)
        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        x0 = -1.5 + yi * 3.0 / 5.0
        y0 = -1.5 + yi * 3.0 / 5.0
        draw_lorenz_for_input_values(ax, dt, n, x0, y0, 1.05)

# změna velikosti komponent v grafu.
plt.tight_layout()

# uložení grafu
plt.savefig("variable_x0_y0_params_multiplot.png")

# zobrazení grafu
plt.show()