希尔伯特曲线信息图

{ "type": "educational mathematical infographic", "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": "large 2D line plot", "right_sidebar": "stacked informational panels and text blocks" }, "main_graph": { "axes": { "x_axis": "labeled 'x (column index)' with ticks 0 to 7", "y_axis": "labeled 'y (row index)' with ticks 0 to 7" }, "grid": "{argument name=\"grid size\" default=\"8x8\"} dashed light gray lines", "curve": { "description": "continuous non-intersecting path filling the grid", "style": "thick line with directional arrows", "colors": "{argument name=\"curve colors\" default=\"gradient transitioning through purple, blue, green, yellow, orange, and red\"}", "markers": [ "purple dot at bottom left labeled '00'", "blue dot at top left labeled '64'" ], "labels": "various two-digit numbers scattered along the path vertices, such as 01, 02, 32, 65, 70" } }, "sidebar": { "sections": [ { "title": "Legend", "type": "box with rounded corners", "count": 4, "items": [ "purple dot: 'Start (step 0)'", "blue dot: 'End (step 63)'", "black arrow: 'Direction of traversal'", "colored lines: 'Curve (colored by sub-quadrant progression)'" ] }, { "title": "Definition", "type": "text block", "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": "Properties", "type": "bulleted list", "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": "Quadrant structure (recursive)", "type": "2x2 colored grid", "count": 4, "boxes": [ "Top-left blue: 'Q2 (steps 32-63)'", "Top-right yellow: 'Q3 (steps 48-63)'", "Bottom-left purple: 'Q0 (steps 0-31)'", "Bottom-right pink: 'Q1 (steps 16-47)'" ], "footer_text": "Each quadrant is a degree-2 Hilbert curve (recursively defined)." } ] } }

{ "type": "教育性数学信息图", "header": { "title": "{argument name=\"main title\" default=\"希尔伯特曲线\"}", "subtitle": "{argument name=\"degree subtitle\" default=\"3 阶 (Order 3)\"}", "equation": "n = 3 -> 2^n x 2^n = 8 x 8 网格，2^(2n) = 64 个步骤" }, "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 (列索引)'，刻度为 0 到 7", "y_axis": "标注为 'y (行索引)'，刻度为 0 到 7" }, "grid": "{argument name=\"grid size\" default=\"8x8\"} 虚线浅灰色网格", "curve": { "description": "填充网格的连续不相交路径", "style": "带有方向箭头的粗线", "colors": "{argument name=\"curve colors\" default=\"从紫色、蓝色、绿色、黄色、橙色到红色的渐变色\"}", "markers": [ "左下角的紫色点，标注为 '00'", "左上角的蓝色点，标注为 '64'" ], "labels": "沿路径顶点散布的各种两位数，例如 01、02、32、65、70" } }, "sidebar": { "sections": [ { "title": "图例", "type": "圆角框", "count": 4, "items": [ "紫色点：'起点 (步骤 0)'", "蓝色点：'终点 (步骤 63)'", "黑色箭头：'遍历方向'", "彩色线条：'曲线 (按子象限进度着色)'" ] }, { "title": "定义", "type": "文本块", "text": "n 阶希尔伯特曲线将单位区间 [0,1] 映射到单位正方形 [0,1]x[0,1]，同时保持局部性。" }, { "title": "属性", "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", "总步骤数：64 = 2^{2*3}", "以连续路径精确访问每个 64 个网格点一次。" ] }, { "title": "象限结构 (递归)", "type": "2x2 彩色网格", "count": 4, "boxes": [ "左上蓝色：'Q2 (步骤 32-63)'", "右上黄色：'Q3 (步骤 48-63)'", "左下紫色：'Q0 (步骤 0-31)'", "右下粉色：'Q1 (步骤 16-47)'" ], "footer_text": "每个象限都是一个 2 阶希尔伯特曲线 (递归定义)。" } ] } }