ヒルベルト曲線インフォグラフィック

Generates an educational mathematical diagram explaining a degree 3 Hilbert curve, complete with a plotted graph, legend, and properties.

{
  "type": "教育数学インフォグラフィック",
  "header": {
    "title": "{argument name="main title" default="Hilbert Curve"}",
    "subtitle": "{argument name="degree subtitle" default="Degree 3 (Order 3)"}",
    "equation": "n = 3 -> 2^n x 2^n = 8 x 8 grid, 2^(2n) = 64 steps"
  },
  "layout": {
    "left_panel": "大きな2D線プロット",
    "right_sidebar": "積み重ねられた情報パネルとテキストブロック"
  },
  "main_graph": {
    "axes": {
      "x_axis": "ラベル 'x (column index)' 、目盛り 0 から 7",
      "y_axis": "ラベル 'y (row index)' 、目盛り 0 から 7"
    },
    "grid": "{argument name="grid size" default="8x8"} 点線の薄いグレー線",
    "curve": {
      "description": "グリッドを埋める連続した非交叉パス",
      "style": "方向矢印付きの太い線",
      "colors": "{argument name="curve colors" default="purple, blue, green, yellow, orange, and red through gradient transition"}",
      "markers": [
        "左下の紫ドット、ラベル '00'",
        "左上の青ドット、ラベル '64'"
      ],
      "labels": "パスの頂点に散らばった various two-digit numbers、例: 01, 02, 32, 65, 70"
    }
  },
  "sidebar": {
    "sections": [
      {
        "title": "凡例",
        "type": "丸角ボックス",
        "count": 4,
        "items": [
          "紫ドット: 'Start (step 0)'",
          "青ドット: 'End (step 63)'",
          "黒矢印: 'Direction of traversal'",
          "色付き線: 'Curve (colored by sub-quadrant progression)'"
        ]
      },
      {
        "title": "定義",
        "type": "テキストブロック",
        "text": "Hilbert curve of degree n maps the unit interval [0,1] onto the unit square [0,1]x[0,1] while preserving locality."
      },
      {
        "title": "性質",
        "type": "箇条書きリスト",
        "heading": "For degree 3:",
        "count": 3,
        "items": [
          "Grid size: 8 x 8 = 2^3 x 2^3",
          "Total steps: 64 = 2^{2*3}",
          "Visits each of the 64 grid points exactly once in a continuous path."
        ]
      },
      {
        "title": "象限構造 (再帰的)",
        "type": "2x2カラーグリッド",
        "count": 4,
        "boxes": [
          "左上青: 'Q2 (steps 32-63)'",
          "右上黄: 'Q3 (steps 48-63)'",
          "左下紫: 'Q0 (steps 0-31)'",
          "右下ピンク: 'Q1 (steps 16-47)'"
        ],
        "footer_text": "Each quadrant is a degree-2 Hilbert curve (recursively defined)."
      }
    ]
  }
}

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