{
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  {
   "cell_type": "markdown",
   "id": "0",
   "metadata": {},
   "source": [
    "# Tutorial 5 - 3D plotting\n",
    "\n",
    "This tutorial draws a Lorenz System, it reproduces a tutorial from [Tikz-Python](https://github.com/ltrujello/Tikz-Python/blob/main/examples/lorenz/lorenz.py)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tikzpics import TikzFigure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# source: https://github.com/ltrujello/Tikz-Python/blob/main/examples/lorenz/lorenz.py\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "\n",
    "# lorenz parameters\n",
    "rho = 28.0\n",
    "sigma = 10.0\n",
    "beta = 8.0 / 3.0\n",
    "\n",
    "\n",
    "# Next state according to the ODEs\n",
    "def next(*state):\n",
    "    x, y, z = state[0][0], state[0][1], state[0][2]\n",
    "    return sigma * (y - x), x * (rho - z) - y, x * y - beta * z\n",
    "\n",
    "\n",
    "# Set initial conditions and time steps\n",
    "initial = [1.0, 1.0, 1.0]\n",
    "t = np.arange(0.0, 20.0, 0.01)\n",
    "\n",
    "# Solve for the next positions, scale them\n",
    "states = odeint(func=next, y0=initial, t=t)\n",
    "states = states * 0.25\n",
    "\n",
    "xvec = states[:, 0]\n",
    "yvec = states[:, 1]\n",
    "zvec = states[:, 2]\n",
    "\n",
    "# Plot the lorenz system\n",
    "fig = TikzFigure(ndim=3)\n",
    "options = [\"color=black\", \"thick\"]\n",
    "\n",
    "fig.plot3d(xvec, yvec, zvec, options=options, layer=0)\n",
    "fig.add_node(\n",
    "    x=xvec[0],\n",
    "    y=yvec[0],\n",
    "    z=zvec[0],\n",
    "    fill=\"green!50!black\",\n",
    "    inner_sep=\"2.0pt\",\n",
    "    options=\"circle\",\n",
    ")\n",
    "fig.add_node(\n",
    "    x=xvec[-1],\n",
    "    y=yvec[-1],\n",
    "    z=zvec[-1],\n",
    "    fill=\"red!50!black\",\n",
    "    inner_sep=\"2.0pt\",\n",
    "    options=\"circle\",\n",
    ")\n",
    "\n",
    "fig.show(width=500)"
   ]
  }
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