希尔伯特曲线数学信息图表

{
  "type": "教育数学信息图表",
  "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": "大型二维线图",
    "right_sidebar": "堆叠式信息面板与文本块"
  },
  "main_graph": {
    "axes": {
      "x_axis": "标有刻度 0 至 7 的 'x (column index)' 轴",
      "y_axis": "标有刻度 0 至 7 的 'y (row index)' 轴"
    },
    "grid": "[8x8] 浅灰色虚线网格",
    "curve": {
      "description": "完全填满网格且无自交的连续空间填充路径",
      "style": "带有细微方向指示箭头的清晰粗线",
      "colors": "[紫、蓝、绿、黄、橙、红渐变过渡]",
      "markers": [
        "左下角标有 '00' 的紫色圆点",
        "左上角标有 '63' 的蓝色圆点"
      ],
      "labels": "分布在关键顶点上的两位数步进序号标签，如 01、02、16、32、48、63"
    }
  },
  "sidebar": {
    "sections": [
      {
        "title": "Legend",
        "type": "圆角框",
        "items": [
          "紫色圆点: 'Start (step 0)'",
          "蓝色圆点: 'End (step 63)'",
          "黑色箭头: 'Direction of traversal'",
          "彩色线条: 'Curve (colored by sub-quadrant progression)'"
        ]
      },
      {
        "title": "Definition",
        "type": "文本块",
        "text": "n阶希尔伯特曲线在保持局部性的同时，将一维单位区间 [0,1] 连续映射到单位正方形 [0,1]x[0,1]。"
      },
      {
        "title": "Properties",
        "type": "项目符号列表",
        "heading": "For degree 3:",
        "items": [
          "Grid size: 8 x 8 = 2^3 x 2^3",
          "Total steps: 64 = 2^(2*3)",
          "以单条连续路径无重复遍历全部64个离散网格点。"
        ]
      },
      {
        "title": "Quadrant structure (recursive)",
        "type": "2x2 彩色微缩网格图",
        "boxes": [
          "左上蓝色: 'Q2 (steps 32-47)'",
          "右上黄色: 'Q3 (steps 48-63)'",
          "左下紫色: 'Q0 (steps 0-15)'",
          "右下粉色: 'Q1 (steps 16-31)'"
        ],
        "footer_text": "每个象限均由经过旋转变换的2阶希尔伯特曲线递归构成。"
      }
    ]
  }
}