[
  {
    "fn": "math::atoms::carpet_2d",
    "in": {
      "n": 3
    },
    "out": {
      "shape": [
        3,
        3
      ],
      "data": [
        1,
        1,
        1,
        1,
        0,
        1,
        1,
        1,
        1
      ]
    },
    "note": "the 3 by 3 seed every carpet design rests on"
  },
  {
    "fn": "math::two::carpet",
    "in": {
      "number": 3,
      "level": 2
    },
    "out": {
      "v": 1,
      "width": 9,
      "height": 9,
      "types": [
        [
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        [
          1,
          0,
          1,
          1,
          0,
          1,
          1,
          0,
          1
        ],
        [
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        [
          1,
          1,
          1,
          0,
          0,
          0,
          1,
          1,
          1
        ],
        [
          1,
          0,
          1,
          0,
          0,
          0,
          1,
          0,
          1
        ],
        [
          1,
          1,
          1,
          0,
          0,
          0,
          1,
          1,
          1
        ],
        [
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        [
          1,
          0,
          1,
          1,
          0,
          1,
          1,
          0,
          1
        ],
        [
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ]
      ]
    },
    "note": "the byte-grid crossing: the cell as math::two::to_json writes it"
  },
  {
    "fn": "math::two::census::census",
    "in": {
      "cell": {
        "fn": "math::two::carpet",
        "in": {
          "number": 3,
          "level": 2
        }
      }
    },
    "out": {
      "fills": 64,
      "voids": 17,
      "perimeter": 80,
      "vertices": 96,
      "edges": 168,
      "euler": -8
    },
    "note": "a struct crossing: the Census through its serde derive"
  },
  {
    "fn": "math::counts::fill",
    "in": {
      "code": "23",
      "number": 3,
      "dimension": 3,
      "level": 2,
      "base": 2
    },
    "out": "400",
    "note": "the sponge's filled cells in closed form, u128 as a decimal string"
  },
  {
    "fn": "math::bang::bang",
    "in": {
      "dimension": 3
    },
    "out": 22,
    "note": "Universe::distinct() of the dimension-3 universe"
  },
  {
    "fn": "math::three::census::census",
    "in": {
      "cell": {
        "fn": "math::three::carpet",
        "in": {
          "number": 3,
          "level": 1
        }
      }
    },
    "out": "72",
    "note": "the .surface field only, u128 as a decimal string"
  },
  {
    "fn": "math::spectrum::laplacian_spectrum",
    "in": {
      "network": {
        "dim": 1,
        "nodes": [
          [
            0.0
          ],
          [
            1.0
          ],
          [
            2.0
          ],
          [
            3.0
          ],
          [
            4.0
          ]
        ],
        "branches": [
          [
            0,
            1,
            1.0
          ],
          [
            1,
            2,
            1.0
          ],
          [
            2,
            3,
            1.0
          ],
          [
            3,
            4,
            1.0
          ]
        ]
      },
      "normalised": false
    },
    "out": [
      0.0,
      0.38196601125,
      1.38196601125,
      2.61803398875,
      3.61803398875
    ],
    "note": "the five eigenvalues of a 5-node path, ascending, to 12 decimals"
  }
]