Hilbert Curve Infographic

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)'",       ...