{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 04: Dzyaloshinskii-Moriya energy term\n",
    "\n",
    "> Interactive online tutorial:\n",
    "> [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/ubermag/oommfc/master?filepath=docs%2Fipynb%2Findex.ipynb)\n",
    "\n",
    "Dzyaloshinskii-Moriya energy density, depending on the crystallographic class, is computed as\n",
    "\n",
    "$$\\mathbf{w_\\text{dmi}} = \\left\\{\n",
    "\\begin{array}{ll}\n",
    "D \\mathbf{m} \\cdot (\\nabla \\times \\mathbf{m}), & \\text{for}\\,\\,T(O) \\\\\n",
    "D ( \\mathbf{m} \\cdot \\nabla m_{z} - m_{z} \\nabla \\cdot \\mathbf{m}), & \\text{for}\\,\\,C_{nv} \\\\\n",
    "D\\mathbf{m} \\cdot \\left( \\frac{\\partial \\mathbf{m}}{\\partial x} \\times \\hat{x} - \\frac{\\partial \\mathbf{m}}{\\partial y} \\times \\hat{y} \\right), & \\text{for}\\,\\,D_{2d} \\\\\n",
    "\\end{array}\n",
    "\\right. $$\n",
    "\n",
    "where $\\mathbf{m}$ is the normalised ($|\\mathbf{m}|=1$) magnetisation, and $D$ is the DM energy constant. DMI energy term tends to align neighbouring magnetic moments perpendicular to each other.\n",
    "\n",
    "In `oommfc`, $\\mathbf{m}$ is a part of the magnetisation field `system.m`. Therefore, only DMI energy constant $D$ should be provided as an input parameter to uniquely define the Exchange energy term. $D$ can be constant in space or spatially varying.\n",
    "\n",
    "## Spatially constant $D$\n",
    "\n",
    "Let us start by assembling a simple simple simulation where $D$ does not vary in space. The sample is a \"one-dimensional\" chain of magnetic moments. We are going to choose $C_{nv}$ as the crystallographic class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import oommfc as oc\n",
    "import discretisedfield as df\n",
    "import micromagneticmodel as mm\n",
    "%matplotlib inline\n",
    "\n",
    "p1 = (-10e-9, 0, 0)\n",
    "p2 = (10e-9, 1e-9, 1e-9)\n",
    "cell = (1e-9, 1e-9, 1e-9)\n",
    "region = df.Region(p1=p1, p2=p2)\n",
    "mesh = df.Mesh(region=region, cell=cell)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mesh is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2b0a75f5c4184c42b72693fdd774b909",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mesh.k3d()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system has a Hamiltonian, which consists of only DMI energy term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = 1e-3  # Dzyaloshinksii-Moriya energy constant (J/m**2)\n",
    "system = mm.System(name='dmi_constant_D')\n",
    "system.energy = mm.DMI(D=D, crystalclass='Cnv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to minimise the system's energy using `oommfc.MinDriver` later. Therefore, we do not have to define the system's dynamics equation. Finally, we need to define the system's magnetisation (`system.m`). We are going to make it random with $M_\\text{s}=8\\times10^{5} \\,\\text{Am}^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import discretisedfield as df\n",
    "\n",
    "Ms = 8e5  # saturation magnetisation (A/m)\n",
    "\n",
    "def m_fun(pos):\n",
    "    \"\"\"Return random 3d vectors for initial random magnetisation\"\"\"\n",
    "    return [2*random.random()-1, 2*random.random()-1, 2*random.random()-1]\n",
    "\n",
    "system.m = df.Field(mesh, dim=3, value=m_fun, norm=Ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magnetisation, we have set as initial values looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "08b91a8c295745388a3516de3e771615",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)  # k3d plot\n",
    "system.m.plane('y').mpl()                     # matplotlib plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can minimise the system's energy by using `oommfc.MinDriver`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020/03/09 10:51: Running OOMMF (dmi_constant_D.mif) ... (1.0 s)\n"
     ]
    }
   ],
   "source": [
    "md = oc.MinDriver()\n",
    "md.drive(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect that now all magnetic moments are aligned orthogonally to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e031aa016128400ca7e7162aa00ae21c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)  # k3d plot\n",
    "system.m.plane('y').mpl()                     # matplotlib plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spatially varying $D$\n",
    "\n",
    "In the case of DMI, there is only one way how a parameter can be made spatially varying - using a dictionary.\n",
    "\n",
    "In order to define a parameter using a dictionary, regions must be defined in the mesh. Regions are defined as a dictionary, whose keys are the strings and values are `discretisedfield.Region` objects, which take two corner points of the region as input parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "p1 = (-10e-9, 0, 0)\n",
    "p2 = (10e-9, 1e-9, 1e-9)\n",
    "cell = (1e-9, 1e-9, 1e-9)\n",
    "subregions = {'region1': df.Region(p1=(-10e-9, 0, 0), p2=(0, 1e-9, 1e-9)),\n",
    "              'region2': df.Region(p1=(0, 0, 0), p2=(10e-9, 1e-9, 1e-9))}\n",
    "region = df.Region(p1=p1, p2=p2)\n",
    "mesh = df.Mesh(region=region, cell=cell, subregions=subregions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regions we have defined are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b04c2e4ee1f84074b4e3189eee7bb60b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mesh.k3d_subregions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us say there is no DMI energy ($D=0$) in region 1, whereas in region 2 $D=10^{-3} \\,\\text{Jm}^{-2}$. Unlike Zeeman and anisotropy energy terms, the DMI energy constant is defined between cells. Therefore, it is necessary to also define the value of $D$ between the two regions. This is achieved by adding another item to the dictionary with key `'region1:region2'`. The object `D` is now defined as a dictionary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = {'region1': 0, 'region2': 1e-3, 'region1:region2': 0.5e-3}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system object is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "system = mm.System(name='dmi_dict_D')\n",
    "system.energy = mm.DMI(D=D, crystalclass='Cnv')\n",
    "system.m = df.Field(mesh, dim=3, value=m_fun, norm=Ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Its initial (and random) magnetisation is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "99bd64ac6ac24b499103a03576a28d94",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)\n",
    "system.m.plane('y').mpl()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we minimise the energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020/03/09 10:51: Running OOMMF (dmi_dict_D.mif) ... (1.0 s)\n"
     ]
    }
   ],
   "source": [
    "md.drive(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magnetisation is as we expected. The magnetisation remains random in region 1, and it is orthogonally aligned in region 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f3438a01e2f74f85b55fca8cea8e54d3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)\n",
    "system.m.plane('y').mpl()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "08b91a8c295745388a3516de3e771615": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_f9331c66056a4bcb9daf01a16f6f3acd",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "45c44170502144788056d1f287de3c85",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "0ee8dc4bd69f42a4a4a0e6853978af68": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "11003643a0c34ad696b07ac4ff0dbf2c": {
      "buffers": [
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "opacities",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYJA4yMDAYA/BHEjsDwdgbEaGCwcQ4huQ2BOQ1CQgiSsgsQ/sR7AZkNlI+AASW8EByUwHJLuQ2BuQ1FxAEv+AxOZwRLAl4GwAunIcnQ==",
        "encoding": "base64",
        "path": [
         "positions",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "color": 5010096,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         0
        ]
       },
       "compression_level": 0,
       "id": 139811457703056,
       "mesh_detail": 2,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Points #1",
       "opacities": {
        "dtype": "float32",
        "shape": [
         0
        ]
       },
       "opacity": 1,
       "point_size": 0.25,
       "positions": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "shader": "3dSpecular",
       "type": "Points",
       "visible": true
      }
     },
     "1db9d463fe184daeb32ab87efaf9e484": {
      "buffers": [
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "opacities",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYJA4yMDAYA/BHEjsDwdgbEaGCwcQ4huQ2BOQ1CQgiSsgsQ/sR7AZkNlI+AASW8EByUwHJLuQ2BuQ1FxAEv+AxOZwRLAl4GwAunIcnQ==",
        "encoding": "base64",
        "path": [
         "positions",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "color": 5010096,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         0
        ]
       },
       "compression_level": 0,
       "id": 139810261126032,
       "mesh_detail": 2,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Points #1",
       "opacities": {
        "dtype": "float32",
        "shape": [
         0
        ]
       },
       "opacity": 1,
       "point_size": 0.25,
       "positions": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "shader": "3dSpecular",
       "type": "Points",
       "visible": true
      }
     },
     "2b0a75f5c4184c42b72693fdd774b909": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_72aa9342215144a89a905937f69c33f7",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "802642ac298d42b4866d9897a4dec6f6",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "3429b6aae1c647bf8ec6695f25c56880": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.438107694716017,
        -24.139634900585953,
        2.1426422671631706,
        0.011684417724609375,
        0.5000000149011612,
        0.49999993946403265,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_d93926ad5769419faf4e2859806afbce",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139810261138768,
        139810261126032
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "38b476cd2198445ea70ed789ad2c17c3": {
      "buffers": [
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "opacities",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYJA4yMDAYA/BHEjsDwdgbEaGCwcQ4huQ2BOQ1CQgiSsgsQ/sR7AZkNlI+AASW8EByUwHJLuQ2BuQ1FxAEv+AxOZwRLAl4GwAunIcnQ==",
        "encoding": "base64",
        "path": [
         "positions",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "color": 5010096,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         0
        ]
       },
       "compression_level": 0,
       "id": 139810254640784,
       "mesh_detail": 2,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Points #1",
       "opacities": {
        "dtype": "float32",
        "shape": [
         0
        ]
       },
       "opacity": 1,
       "point_size": 0.25,
       "positions": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "shader": "3dSpecular",
       "type": "Points",
       "visible": true
      }
     },
     "3d1f3e2882904d24a404082080ea8dd3": {
      "buffers": [
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoDAAAAAAE=",
        "encoding": "base64",
        "path": [
         "opacities",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYJA4yMDAYA/BHEjsDwdgbEaGCwcQ4huQ2BOQ1CQgiSsgsQ/sR7AZkNlI+AASW8EByUwHJLuQ2BuQ1FxAEv+AxOZwRLAl4GwAunIcnQ==",
        "encoding": "base64",
        "path": [
         "positions",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "color": 5010096,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         0
        ]
       },
       "compression_level": 0,
       "id": 139810330871248,
       "mesh_detail": 2,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Points #1",
       "opacities": {
        "dtype": "float32",
        "shape": [
         0
        ]
       },
       "opacity": 1,
       "point_size": 0.25,
       "positions": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "shader": "3dSpecular",
       "type": "Points",
       "visible": true
      }
     },
     "45c44170502144788056d1f287de3c85": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.671948644907122,
        -24.412233939557666,
        2.1608156237394427,
        0.06379270553588867,
        0.4999999694991857,
        0.5000000298023224,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_4ce22317f07d40aeb7b6790cbfbeade4",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139810331030608,
        139811457703056
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "4ce22317f07d40aeb7b6790cbfbeade4": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "59e116fe920440a386df5ce26d3310d9": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.707952969879074,
        -24.636929444760327,
        2.175795296317352,
        -0.04999999329447746,
        0.5,
        0.5,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_dce2ef66bed14babb2ec7f9f93a22993",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139811457479824
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "6119867aa73b4bbdb8d97683115a8ae2": {
      "buffers": [
       {
        "data": "eNrzU2Jg8APizM2HwNjixT8wzvGyAWO/AZYHAK/CNa0=",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNrrnCV8kIGBwf7v/3p7IA1m+yxKs3t36scBEJuBwcGEkeEBmJ0b7mYvZLr8AEJ9A5jtB1R/Z2ohVD2DCVAPmJ0NVO99Zc5+EPsfWP2BzSB2BFB9DBBD1B8wBpoD0mefCVR/a6qhA0QcJNYAZscB1QqbtkPFGYDqF4DZGUD1707dQFLP4AhipwDVd81idoSqBwIBMDsNqB4AGJA81Q==",
        "encoding": "base64",
        "path": [
         "origins",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNq7tY5nf9vWDKNf/+v3g7BVU/S6W+t47EH4XPlEfaCYPQjzX1ZZDxTbD8Jn3U4ZwNQr2S7ceBOo9joQv7q23OAPUC0Ia9Y3r70GVHsFiAW4/636C1QLwmu5e9YDxewvAbFEhPk6oJj9fyC+eTRWHyi2/yIQr/32UA8oth+EfeuTNgDF7EH47W/mTf+h6m8tSdt4Aaj2PBC3uFkZMjA07AfhU7vyjc4B1Z4F4uBdzzYBxexBeJFfqxFQbD8AYVOEsw==",
        "encoding": "base64",
        "path": [
         "vectors",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         20,
         2
        ]
       },
       "compression_level": 0,
       "head_color": 255,
       "head_size": 1,
       "id": 139810296446864,
       "label_size": 1,
       "labels": [],
       "line_width": 0.01,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Vectors #1",
       "origin_color": 255,
       "origins": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "type": "Vectors",
       "use_head": true,
       "vectors": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "visible": true
      }
     },
     "635886f61a5e4baba9288330237cb7b0": {
      "buffers": [
       {
        "data": "eNrLjQ1nyAXifAMGME7cfxGMiwsLwDjH1xGMc2PCwDj28DUwzvGyAeMCYw4whunLt1IAYz8lBjCuqG8AY6+rb8E4x90CjP0vvQDjHE9rMK7ongjGFi/+gXFlYzMYAwCzhzTj",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoB8AAP/1KKHsGiLU8/iaQpP7ozCcGoO1s/WEtlPxuC+sC+o1E/gPNePgEA4MA+j6A+sRsRP8JmsMDATHo/OCM/PySAlMDgrRU8+DQrP2CacsCF4FY/BI9NPqNHAsC8SN0+HTtDP1jPmr+TNUA//G1gPwkEBL+gCCw9RtBfPhe2Wj9wojg/srRWPydlzT/C2Xw+RHx2P+RSP0CLDTk/VeT/PqlLa0B8ABw+VrQEPmD9hUBGZyU+CvFGP+xEpEAwUqg+KDwVPjua00D25HM/On9EP2uc6UCy7n4/GLHhPkZsCkHwsl8+xFaKPemUIEFbhQk/Zqb5PiGHZI4=",
        "encoding": "base64",
        "path": [
         "origins",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoB8AAP/0xKUT9EWx6/JJKmvvbcGT5Rdza/sJZKv64hKD99RyO/QIYQPwAAgD+F4b4+h90IviyEzTyBmXS/4oz8vowEkD6RUns/3tOsvvTSFD8KwS2/fjgZP+jCbb8O3Qo+OnYGv6LCFL8mawC/99tAvyiBAD3sfmo/3RcQPy5sNb/AieK+ZGktv3NSVr4fkwE/h/hsvx2Xer8rNuS+4lfdOXq6tL7C/zE/1aU9P/4pID9dTC0/FOINvz+xOz+hW68+7GE1P22OZr7ryWe/df4Iv5VyzD5l3X2/P3fyPX4Rm76IJhA/T2pdP5BOib+2VZi9RzPLPCYJcGw=",
        "encoding": "base64",
        "path": [
         "vectors",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         20,
         2
        ]
       },
       "compression_level": 0,
       "head_color": 255,
       "head_size": 1,
       "id": 139810331030608,
       "label_size": 1,
       "labels": [],
       "line_width": 0.01,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Vectors #1",
       "origin_color": 255,
       "origins": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "type": "Vectors",
       "use_head": true,
       "vectors": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "visible": true
      }
     },
     "66de16c730264f91a43361a982d689c1": {
      "buffers": [
       {
        "data": "eNrLN5dgyAfhldvA2E+JAYwLDSE4SRuCc0J9wDjfSg6MPa6/B2OLF//AuHDJejAuKy8HY5i+goxUMI44cReMo47fBuOc8AAwrmjtBON8KwUwLjRiBOPwU/fBGADRWDI5",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoB8AAP/z9qEsHWWR4/0dRkP774DcHy8jo+5GeMPmMQ7MBP3tc+QHuCP4+d0sAark8/P9huP176p8ARFdY+3np4P5NFh8DgN2g/dMI5Pz1qYMDng2E/JchhP6qrDsA6Wq0+mM9+PQap2b+hcgc/AAAAAIL2AL7cXVU//rSZPlHIPD+QEYo8fvsIP/x4qT+CsDE/V7l4P43JMUC4JFc9684dP087YUAYLOM9ttUBPohXj0AYy9Q9KowJPjTOvUDiq4E+Abg1P8nP4ECMYR0/p/HpPg9P+kAIn5Y+JnJhPxM/DEFaxTE/AnRtP4cKEkGT2tM+KGz0PZPxapo=",
        "encoding": "base64",
        "path": [
         "origins",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoB8AAP/xe4Mr+uznK+oqlJv8kXPz+HhiI/OTDnPlPne77FhiA+gfaEv4FjJz4zXB+/frBdvyZaAL+7qyc+vfVwv9SmC7/Ab1C/0AnnvoR3VDzOB0O/SpBDv7SiCr+NS6U+DSZgPzFIzT4hVG69AACAP7+EP7+3uyq/BJbMPkQh877nXnc/2LePvR84tD4Kwsa+rnJxv2tMDr9pG2U/V3duvs2mHb36NEc/JRU/P4t3KD06zUo/6zk7PzjjXL87qPw+A+DWvj1+hr9kDGu+xnKwPenwJL/vwdI+TeRCv1fiB79oFce+BOhavxOvPj+0lTA+9uRCP2Stcj4=",
        "encoding": "base64",
        "path": [
         "vectors",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         20,
         2
        ]
       },
       "compression_level": 0,
       "head_color": 255,
       "head_size": 1,
       "id": 139810261138768,
       "label_size": 1,
       "labels": [],
       "line_width": 0.01,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Vectors #1",
       "origin_color": 255,
       "origins": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "type": "Vectors",
       "use_head": true,
       "vectors": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "visible": true
      }
     },
     "6b033b8295c840bbbb3bb06a9f59250d": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.56474467826249,
        -24.254909824019105,
        2.1503272610653035,
        0.06147146224975586,
        0.5,
        0.49999993946403265,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_e9a1585b7e84472b8fad1a7fb450b6aa",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139810254679440,
        139810254640784
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "72aa9342215144a89a905937f69c33f7": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "7dcdfb5190d34b9d97388515a3a178a6": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "7ffae9351d40419585a0724f2f1a3f16": {
      "buffers": [
       {
        "data": "eNrbUOTDENRylyFjRShDkN8Rhs1FjQwJFZMZDnffYujp6WEo2XmG4ezWFAYASmwQpw==",
        "encoding": "base64",
        "path": [
         "color_map",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYFjgyIABGuyhDHs0MXt0dQBzTAOd",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjZIQBJjgAAAEdAB8=",
        "encoding": "base64",
        "path": [
         "voxels",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "colorLegend": false,
       "color_map": {
        "dtype": "uint32",
        "shape": [
         10
        ]
       },
       "compression_level": 0,
       "id": 139811457479824,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Voxels #1",
       "opacity": 1,
       "outlines": false,
       "outlines_color": 0,
       "type": "Voxels",
       "visible": true,
       "voxels": {
        "dtype": "uint8",
        "shape": [
         1,
         1,
         20
        ]
       },
       "wireframe": false
      }
     },
     "802642ac298d42b4866d9897a4dec6f6": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.707952969879074,
        -24.636929444760327,
        2.175795296317352,
        -0.04999999329447746,
        0.5,
        0.5,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_8391ba55da8a4a5cbbc2970206271908",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139810385939408
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "8391ba55da8a4a5cbbc2970206271908": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "960ae4ffd4604e69abf7c7bbc2846f48": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.56326740111602,
        -24.17597986945052,
        2.145065323977074,
        0.11261415481567383,
        0.5,
        0.49999999934704215,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_bc7243dedb5d44b3a3fae13c09efb59d",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139810296446864,
        139810330871248
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "99bd64ac6ac24b499103a03576a28d94": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_0ee8dc4bd69f42a4a4a0e6853978af68",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "3429b6aae1c647bf8ec6695f25c56880",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "b04c2e4ee1f84074b4e3189eee7bb60b": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_fb044ca0774a41dc92488d8922df6cf4",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "59e116fe920440a386df5ce26d3310d9",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "bc7243dedb5d44b3a3fae13c09efb59d": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "d5b2d8e8260645e48d7b6bf8b6181457": {
      "buffers": [
       {
        "data": "eNrLN5dgyAfhldvA2E+JAYwLDSE4SRuCc0J9wDjfSg6MPa6/B2OLF//AOHvDfjC2evATjHP8XcAYpp9ceQAzezQT",
        "encoding": "base64",
        "path": [
         "colors",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYGiwZ8AAxIsBAF7EAv0=",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNqzzxI6eC1Szv7ilRT7fT94D376ZGX3JL3HLlngzQH/e9ftHKqb7PvnXjogtc7f3v5Gnn3cr+UHBEWv2d2rqrCf7Np+4IF5hn3JIUt726yEA8+bE+1VTyTar1rNd8Aqaq3djPN1tmwrb+5fWMRuzwAEDlFP9wAp+yk1JXaTgBjEBorZZE5tBsnb337gZG++w8ABxNa7WmHva1oHZs8Aqn26uB3MFgCqj3q6AMy+AVQvE3MDzDYAql8m9R/MXgBU//kisyOIzQBUv7ZIwBGmHgBuSF0P",
        "encoding": "base64",
        "path": [
         "origins",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNoT32G0f925on2LVnruPylub9/epmRvafDcLvh59b6jbQp2jd9a9jcmq9sZx8jvr9sQu18timH/7tXqdnu/Fuy/sox7/4H8gP0XOJ/vaykPsTnH7rzfa4Lz/i2LuPb3ei+141VLsDf0OGunGJK3l4GhwT5mVeH+DN6lhtsOstpvB+LUg6f0gWIgcfsZCW1rgOL7twKxl4ilTixQLQg//OepswWodhMQu9yZoBMPVAvCfoveam0EqgXhS9I9+kCx/SC8YInThg1AteuB2NRqvlYCUC0IS/0MWQ8U2w8A5GlwLw==",
        "encoding": "base64",
        "path": [
         "vectors",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "colorLegend": false,
       "colors": {
        "dtype": "uint32",
        "shape": [
         20,
         2
        ]
       },
       "compression_level": 0,
       "head_color": 255,
       "head_size": 1,
       "id": 139810254679440,
       "label_size": 1,
       "labels": [],
       "line_width": 0.01,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Vectors #1",
       "origin_color": 255,
       "origins": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "type": "Vectors",
       "use_head": true,
       "vectors": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "visible": true
      }
     },
     "d93926ad5769419faf4e2859806afbce": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "dce2ef66bed14babb2ec7f9f93a22993": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "e031aa016128400ca7e7162aa00ae21c": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_7dcdfb5190d34b9d97388515a3a178a6",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "960ae4ffd4604e69abf7c7bbc2846f48",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "e47b48c9ef504c258b18767cd2c6fbc0": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "e9a1585b7e84472b8fad1a7fb450b6aa": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "f3438a01e2f74f85b55fca8cea8e54d3": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_e47b48c9ef504c258b18767cd2c6fbc0",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "6b033b8295c840bbbb3bb06a9f59250d",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "f6a17604dd3f4b8a85ac47b9d4f416bc": {
      "buffers": [
       {
        "data": "eNrbUOTDENRylwEADvwDIg==",
        "encoding": "base64",
        "path": [
         "color_map",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjYFjgyIABGuyhDHs0MXt0dQBzTAOd",
        "encoding": "base64",
        "path": [
         "model_matrix",
         "compressed_buffer"
        ]
       },
       {
        "data": "eNpjZMQATAAA5wAW",
        "encoding": "base64",
        "path": [
         "voxels",
         "compressed_buffer"
        ]
       }
      ],
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "ObjectModel",
      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
       "_view_name": null,
       "colorLegend": false,
       "color_map": {
        "dtype": "uint32",
        "shape": [
         2
        ]
       },
       "compression_level": 0,
       "id": 139810385939408,
       "model_matrix": {
        "dtype": "float32",
        "shape": [
         4,
         4
        ]
       },
       "name": "Voxels #1",
       "opacity": 1,
       "outlines": false,
       "outlines_color": 0,
       "type": "Voxels",
       "visible": true,
       "voxels": {
        "dtype": "uint8",
        "shape": [
         1,
         1,
         20
        ]
       },
       "wireframe": false
      }
     },
     "f9331c66056a4bcb9daf01a16f6f3acd": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "fb044ca0774a41dc92488d8922df6cf4": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}