Hilbert Curve (Space-Filling)
A classic space-filling fractal curve. A single continuous line that visits every point inside a square — without self-intersections. Great for dense infill patterns, map-style decorations, and single-path prints that never lift the nozzle.
Parameters
Hilbert Curve parameters
Size- Width and height of the square bounding box in mm. Range 10–300, step 10, default 100. The curve is centered on the origin and fully contained in the square.
Order (Iterations)- Recursive depth of the curve. Range 1–7, default 4. Each step quadruples the number of line segments — order 1 has 4 segments, order 4 has 256, order 7 has 16 384.
The line length grows exponentially with order. For a 100 mm square:
- Order 1: ~4 segments, chunky zigzag.
- Order 4: ~256 segments, clearly fractal.
- Order 7: ~16 000 segments — fully covers the square like solid infill.
Typical use
- Single-path infill — prints as one continuous extrusion, zero travel moves.
- Map-style graphics — the recursive Hilbert pattern mimics urban street grids.
- Abstract art — higher orders look like dense fabric.
Related
- Fabric Sculpt Overview
- Grid Lattice — simpler rectilinear grid.
- Voronoi Mesh — organic space-filling alternative.