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        "\n# Lorenz attractor\n\nThis is an example of plotting Edward Lorenz's 1963 `\"Deterministic Nonperiodic\nFlow\"`_ in a 3-dimensional space using mplot3d.\n\n   https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Because this is a simple non-linear ODE, it would be more easily done using\n   SciPy's ODE solver, but this approach depends only upon NumPy.</p></div>\n"
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    {
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      "execution_count": null,
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      "source": [
        "import matplotlib.pyplot as plt\nimport numpy as np\n\n\ndef lorenz(xyz, *, s=10, r=28, b=2.667):\n    \"\"\"\n    Parameters\n    ----------\n    xyz : array-like, shape (3,)\n       Point of interest in three-dimensional space.\n    s, r, b : float\n       Parameters defining the Lorenz attractor.\n\n    Returns\n    -------\n    xyz_dot : array, shape (3,)\n       Values of the Lorenz attractor's partial derivatives at *xyz*.\n    \"\"\"\n    x, y, z = xyz\n    x_dot = s*(y - x)\n    y_dot = r*x - y - x*z\n    z_dot = x*y - b*z\n    return np.array([x_dot, y_dot, z_dot])\n\n\ndt = 0.01\nnum_steps = 10000\n\nxyzs = np.empty((num_steps + 1, 3))  # Need one more for the initial values\nxyzs[0] = (0., 1., 1.05)  # Set initial values\n# Step through \"time\", calculating the partial derivatives at the current point\n# and using them to estimate the next point\nfor i in range(num_steps):\n    xyzs[i + 1] = xyzs[i] + lorenz(xyzs[i]) * dt\n\n# Plot\nax = plt.figure().add_subplot(projection='3d')\n\nax.plot(*xyzs.T, lw=0.5)\nax.set_xlabel(\"X Axis\")\nax.set_ylabel(\"Y Axis\")\nax.set_zlabel(\"Z Axis\")\nax.set_title(\"Lorenz Attractor\")\n\nplt.show()"
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      "metadata": {},
      "source": [
        ".. tags::\n   plot-type: 3D,\n   level: intermediate\n\n"
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