Hilbert Curve Infographic

원본 문서

GPT Image 2 · en

{
  "type": "Educational Mathematics Infographics",
  "header": {
    "title": "{argument name=\"main title\" default=\"Hilbert curve\"}",
    "subtitle": "{argument name=\"degree subtitle\" default=\"Order 3\"}",
    "equation": "n = 3 -> 2^n x 2^n = 8 x 8 grid, 2^(2n) = 64 steps"
  },
  "layout": {
    "left_panel": "Large 2D line chart",
    "right_sidebar": "Stacked information panels and text blocks"
  },
  "main_graph": {
    "axes": {
      "x_axis": "Labeled as 'x (column index)', with scales from 0 to 7.",
      "y_axis": "Labeled as 'y (row index)', with scales from 0 to 7."
    },
    "grid": "{argument name=\"grid size\" default=\"8x8\"} Dashed light gray grid",
    "curve": {
      "description": "Continuous non-intersecting paths in a filled mesh",
      "style": "Thick lines with directional arrows",
      "colors": "{argument name=\"curve colors\" default=\"A gradient of colors from purple, blue, green, yellow, orange to red.\"}",
      "markers": [
        "The purple dot in the bottom left corner is marked '00'.",
        "The blue dot in the top left corner is labeled '64'."
      ],
      "labels": "Various two-digit numbers scattered along the path vertices, such as 01, 02, 32, 65, 70."
    }
  },
  "sidebar": {
    "sections": [
      {
        "title": "legend",
        "type": "Rounded corner frame",
        "count": 4,
        "items": [
          "Purple dot: 'Starting point (step 0)'",
          "Blue dot: 'End point (step 63)'",
          "Black arrow: 'Traversal direction'",
          "Colored lines: 'Curves (colored according to sub-quadrant progress)'"
        ]
      },
      {
        "title": "definition",
        "type": "text block",
        "text": "The nth-order Hilbert curve maps the unit interval [0,1] to the unit square [0,1]x[0,1] while preserving locality."
      },
      {
        "title": "property",
        "type": "Bullet List",
        "heading": "For order 3:",
        "count": 3,
        "items": [
          "Grid size: 8 x 8 = 2^3 x 2^3",
          "Total number of steps: 64 = 2^{2*3}",
          "Each of the 64 grid points is accessed precisely once using 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)'",
          "Pink in the bottom right corner: 'Q1 (Steps 16-47)'"
        ],
        "footer_text": "Each quadrant is a second-order Hilbert curve (recursively defined)."
      }
    ]
  }
}

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