希爾伯特曲線圖
Generates an educational mathematical diagram explaining a degree 3 Hilbert curve, complete with a plotted graph, legend, and properties.
Prompt
{
"type": "教育數學資訊圖",
"header": {
"title": "{argument name=\"main title\" default=\"希爾伯特曲線\"}",
"subtitle": "{argument name=\"degree subtitle\" default=\"三階（階數 3）\"}",
"equation": "n = 3 -> 2^n x 2^n = 8 x 8 格，2^(2n) = 64 步"
},
"layout": {
"left_panel": "大型二維線圖",
"right_sidebar": "堆疊資訊面板和文字區塊"
},
"main_graph": {
"axes": {
"x_axis": "標記為 'x (列索引)'，刻度 0 到 7",
"y_axis": "標記為 'y (行索引)'，刻度 0 到 7"
},
"grid": "{argument name=\"grid size\" default=\"8x8\"} 虛線淺灰色線",
"curve": {
"description": "連續不交叉路徑填充網格",
"style": "粗線帶有方向箭頭",
"colors": "{argument name=\"curve colors\" default=\"漸變過渡紫色、藍色、綠色、黃色、橙色和紅色\"}",
"markers": [
"左下角紫色圓點標記為 '00'",
"左上角藍色圓點標記為 '64'"
],
"labels": "沿路徑頂點分佈的各種兩位數，如 01、02、32、65、70"
}
},
"sidebar": {
"sections": [
{
"title": "圖例",
"type": "圓角方框",
"count": 4,
"items": [
"紫色圓點：'起點（步驟 0）'",
"藍色圓點：'終點（步驟 63）'",
"黑色箭頭：'遍歷方向'",
"彩色線：'曲線（按子象限進展著色）'"
]
},
{
"title": "定義",
"type": "文字區塊",
"text": "希爾伯特曲線階數 n 將單位區間 [0,1] 映射到單位正方形 [0,1]x[0,1]，同時保留局部性。"
},
{
"title": "性質",
"type": "項目符號列表",
"heading": "對於三階：",
"count": 3,
"items": [
"網格大小：8 x 8 = 2^3 x 2^3",
"總步數：64 = 2^{2*3}",
"在連續路徑中每個網格點恰好訪問一次。"
]
},
{
"title": "象限結構（遞迴）",
"type": "2x2 彩色網格",
"count": 4,
"boxes": [
"左上藍色：'Q2（步驟 32-63）'",
"右上黃色：'Q3（步驟 48-63）'",
"左下紫色：'Q0（步驟 0-31）'",
"右下粉色：'Q1（步驟 16-47）'"
],
"footer_text": "每個象限是一個二階希爾伯特曲線（遞迴定義）。"
}
]
}
}
機器翻譯 — 實際產出作品的是原文 prompt。
原文 Prompt
{
"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)."
}
]
}
}