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)."
}
]
}
}