希尔伯特曲线信息图

提示词

{   "type": "教育数学信息图",   "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 网格, 2^(2n) = 64 步"   },   "layout": {     "left_panel": "大型二维线图",     "right_sidebar": "堆叠的信息面板和文本块"   },   "main_graph": {     "axes": {       "x_axis": "标注为 'x (column index)'，刻度从 0 到 7",       "y_axis": "标注为 'y (row index)'，刻度从 0 到 7"     },     "grid": "{argument name=\"grid size\" default=\"8x8\"} 虚线浅灰色网格线",     "curve": {       "description": "连续的不相交路径，填满整个网格",       "style": "带方向箭头的粗线",       "colors": "{argument name=\"curve colors\" default=\"gradient transitioning through purple, blue, green, yellow, orange, and red\"}",       "markers": [         "左下角紫色圆点，标注为 '00'",         "左上角蓝色圆点，标注为 '64'"       ],       "labels": "沿路径顶点散布的各种两位数字，例如 01、02、32、65、70"     }   },   "sidebar": {     "sections": [       {         "title": "图例",         "type": "带圆角的框",         "count": 4,         "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": "定义",         "type": "文本块",         "text": "n 阶 Hilbert 曲线将单位区间 [0,1] 映射到单位正方形 [0,1]x[0,1]，同时保持局部性。"       },       {         "title": "性质",         "type": "项目符号列表",         "heading": "对于 3 阶：",         "count": 3,         "items": [           "网格大小：8 x 8 = 2^3 x 2^3",           "总步数：64 = 2^{2*3}",           "在一条连续路径中恰好一次访问 64 个网格点中的每一个。"         ]       },       {         "title": "象限结构（递归）",         "type": "2x2 彩色网格",         "count": 4,         "boxes": [           "左上蓝色：'Q2 (steps 32-63)'",           "右上黄色：'Q3 (steps 48-63)'",           "左下紫色：'Q0 (steps 0-31)'",           "右下粉色：'Q1 (steps 16-47)'"         ],         "footer_text": "每个象限都是一个 2 阶 Hilbert 曲线（递归定义）。"       }     ]   } }