.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_gallery_mplot3d_lorenz_attractor.py: ================ Lorenz Attractor ================ This is an example of plotting Edward Lorenz's 1963 `"Deterministic Nonperiodic Flow" `_ in a 3-dimensional space using mplot3d. Note: Because this is a simple non-linear ODE, it would be more easily done using SciPy's ode solver, but this approach depends only upon NumPy. .. image:: /gallery/mplot3d/images/sphx_glr_lorenz_attractor_001.png :class: sphx-glr-single-img .. code-block:: default import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D def lorenz(x, y, z, s=10, r=28, b=2.667): ''' Given: x, y, z: a point of interest in three dimensional space s, r, b: parameters defining the lorenz attractor Returns: x_dot, y_dot, z_dot: values of the lorenz attractor's partial derivatives at the point x, y, z ''' 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 dt = 0.01 num_steps = 10000 # Need one more for the initial values xs = np.empty((num_steps + 1,)) ys = np.empty((num_steps + 1,)) zs = np.empty((num_steps + 1,)) # Set initial values xs[0], ys[0], zs[0] = (0., 1., 1.05) # Step through "time", calculating the partial derivatives at the current point # and using them to estimate the next point for i in range(num_steps): x_dot, y_dot, z_dot = lorenz(xs[i], ys[i], zs[i]) xs[i + 1] = xs[i] + (x_dot * dt) ys[i + 1] = ys[i] + (y_dot * dt) zs[i + 1] = zs[i] + (z_dot * dt) # Plot fig = plt.figure() ax = fig.gca(projection='3d') ax.plot(xs, ys, zs, lw=0.5) ax.set_xlabel("X Axis") ax.set_ylabel("Y Axis") ax.set_zlabel("Z Axis") ax.set_title("Lorenz Attractor") plt.show() .. _sphx_glr_download_gallery_mplot3d_lorenz_attractor.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download :download:`Download Python source code: lorenz_attractor.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: lorenz_attractor.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature Keywords: matplotlib code example, codex, python plot, pyplot `Gallery generated by Sphinx-Gallery `_