希爾伯特曲線數學資訊圖表

{
  "type": "教育數學資訊圖表",
  "header": {
    "title": "[Hilbert Curve]",
    "subtitle": "[Degree 3 (Order 3)]",
    "equation": "n = 3 -> 2^n x 2^n = 8 x 8 grid, 2^(2n) = 64 steps"
  },
  "layout": {
    "left_panel": "大型二維線圖",
    "right_sidebar": "堆疊式資訊面板與文字塊"
  },
  "main_graph": {
    "axes": {
      "x_axis": "標有刻度 0 至 7 的 'x (column index)' 軸",
      "y_axis": "標有刻度 0 至 7 的 'y (row index)' 軸"
    },
    "grid": "[8x8] 淺灰色虛線網格",
    "curve": {
      "description": "完全填滿網格且無自交的連續空間填充路徑",
      "style": "帶有細微方向指示箭頭的清晰粗線",
      "colors": "[紫、藍、綠、黃、橙、紅漸變過渡]",
      "markers": [
        "左下角標有 '00' 的紫色圓點",
        "左上角標有 '63' 的藍色圓點"
      ],
      "labels": "分佈在關鍵頂點上的兩位數步進序號標籤，如 01、02、16、32、48、63"
    }
  },
  "sidebar": {
    "sections": [
      {
        "title": "Legend",
        "type": "圓角框",
        "items": [
          "紫色圓點: 'Start (step 0)'",
          "藍色圓點: 'End (step 63)'",
          "黑色箭頭: 'Direction of traversal'",
          "彩色線條: 'Curve (colored by sub-quadrant progression)'"
        ]
      },
      {
        "title": "Definition",
        "type": "文字塊",
        "text": "n階希爾伯特曲線在保持區域性性的同時，將一維單位區間 [0,1] 連續對映到單位正方形 [0,1]x[0,1]。"
      },
      {
        "title": "Properties",
        "type": "專案符號列表",
        "heading": "For degree 3:",
        "items": [
          "Grid size: 8 x 8 = 2^3 x 2^3",
          "Total steps: 64 = 2^(2*3)",
          "以單條連續路徑無重複遍歷全部64個離散網格點。"
        ]
      },
      {
        "title": "Quadrant structure (recursive)",
        "type": "2x2 彩色微縮網格圖",
        "boxes": [
          "左上藍色: 'Q2 (steps 32-47)'",
          "右上黃色: 'Q3 (steps 48-63)'",
          "左下紫色: 'Q0 (steps 0-15)'",
          "右下粉色: 'Q1 (steps 16-31)'"
        ],
        "footer_text": "每個象限均由經過旋轉變換的2階希爾伯特曲線遞迴構成。"
      }
    ]
  }
}