Curves that fold and fill

1. Koch snowflake: definition reference · Hausdorff dimension log 4 / log 3 ≈ 1.2619 (boundary curve) · Curve approximation at iteration 5 of the L-system (3,072 segments, turn 60°), filled and fitted to a 448px square.
2. Lévy C curve: definition reference · Hausdorff dimension 2 ≈ 2 (limit set (contains open sets)) · Curve approximation at iteration 14 of the L-system (16,384 segments, turn 45°), stroked at 1.5px and fitted to a 448px square.
3. Heighway dragon: definition reference · Hausdorff dimension 2 ≈ 2 (limit set (space-filling)) · Curve approximation at iteration 14 of the L-system (16,384 segments, turn 90°), stroked at 1.5px and fitted to a 448px square.
4. Hilbert curve: definition reference · Hausdorff dimension 2 ≈ 2 (limit curve (space-filling)) · Curve approximation at iteration 5 of the L-system (1,023 segments, turn 90°), stroked at 6px and fitted to a 448px square.
5. Gosper curve: definition reference · Hausdorff dimension 2 ≈ 2 (limit curve (space-filling)) · Curve approximation at iteration 4 of the L-system (2,401 segments, turn 60°), stroked at 3.5px and fitted to a 448px square.
6. Peano curve: definition reference · Hausdorff dimension 2 ≈ 2 (limit curve (space-filling)) · Curve approximation at iteration 3 of the L-system (728 segments, turn 90°), stroked at 7px and fitted to a 448px square.

Fractal images are illustrations rendered by Fav Tings from each construction’s published definition; a finite image only approximates the infinite object. References are English Wikipedia articles, used as factual cross-references; nothing is copied from them.