Hilbert Curve Explained

{
 "type": "educational mathematical infographic",
 "header": {
 "title": "Hilbert Curve\",
 "subtitle": "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": "8x8\ dashed light gray lines",
 "curve": {
 "description": "continuous non-intersecting path filling the grid",
 "style": "thick line with directional arrows",
 "colors": "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)."
 }
 ]
 }
}