提示詞/GPT Image 提示詞/提示詞詳細資訊圖片提示詞希爾伯特曲線資訊圖表生成解說三次希爾伯特曲線的教育用數學圖表，包含繪製圖形、圖例與特性說明。此提示詞搭配參考圖片使用立即使用讚0瀏覽290收藏1儲存或分享此提示詞，下次就能輕鬆找到分享提示詞提示詞複製{ "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)." } ] } }展開提示詞
