Overview
Introduction
The terdragon curve is a three-segment relative of the Heighway dragon curve, built from a simple L-system rule that folds a line into thirds at each iteration. This tool repeats that same rule six times around a shared center, producing what we call a hexadragon fractal.
As with the quaddragon, there's no single textbook definition for a "hexadragon," so this is our own six-fold extension rather than a term borrowed from a paper or reference. Enter an iteration count and the tool renders the resulting shape as SVG line art you can download.
What Is Generate a Hexadragon Fractal?
A turtle-graphics fractal built from six copies of the terdragon curve's L-system rule, laid out with 60-degree turns between each copy so they radiate around one hexagonal center instead of one terdragon running off in a single direction.
It reuses the terdragon's exact production rule (F becomes F+F-F), just at a 60-degree turn angle instead of the terdragon's usual 120 degrees, starting from a longer axiom that chains six "F+" segments into a closed hexagon shape.
How Generate a Hexadragon Fractal Works
The generator starts from the axiom "F+F+F+F+F+F", six forward segments each followed by a 60-degree left turn, tracing out a plain hexagon outline at zero iterations.
Each F in that string is then replaced by "F+F-F" for as many iterations as you enter, the same substitution the terdragon curve uses, so every one of the six hexagon edges grows its own folded, self-similar detail independently.
The expanded string is walked by a turtle at a fixed 60-degree turn angle, and the resulting line segments are rescaled to fit the SVG viewbox and drawn as one connected path winding around the shared center.
When To Use Generate a Hexadragon Fractal
Use it when you want a hexagonally symmetric variation on the terdragon curve for generative art, tiling patterns, or fractal-geometry demonstrations.
It's a useful teaching example for how the same production rule produces very different overall shapes depending on the axiom and turn angle it's paired with, compare it against a standalone terdragon curve at 120 degrees.
If you need the standard single-armed terdragon curve rather than this six-fold variant, use a plain terdragon or dragon curve tool instead.
Often used alongside Generate a Quaddragon Curve, Generate a Gosper Curve and Generate a Sierpinski Arrowhead Curve.
Features
Advantages
- Produces a hexagonally symmetric silhouette that reads clearly even at moderate iteration counts, thanks to the six repeated arms.
- Reuses the well-understood terdragon production rule, so the fractal detail at each arm is exactly as predictable as the classic curve's.
- Downloadable as both SVG (for further vector editing) and PNG (for quick use anywhere).
Limitations
- Not a term with one agreed-upon mathematical definition, this is our construction and won't match a formula found in a textbook labeled "hexadragon."
- High iteration counts near the maximum of 7 produce dense, tightly folded line art on every arm that can be slow to render.
Examples
Best Practices & Notes
Best Practices
- Start around 2 to 3 iterations to see the hexagonal structure and early folding clearly before increasing toward the denser high end of the range.
- Download the SVG rather than the PNG if you plan to recolor, scale, or further edit the fractal, vector output has no resolution limit.
Developer Notes
Implemented as an L-system preset ("hexadragon-fractal" in l-system-presets.ts) sharing the standard terdragon curve's production rule (F: "F+F-F") but at a 60-degree turn angle instead of the terdragon's 120 degrees, starting from the axiom "F+F+F+F+F+F". Expansion and turtle interpretation both go through the shared generateLSystemCurve/drawLSystem engine used by every other L-system tool in this category, capped at 7 iterations before geometry normalization and SVG rendering.
Generate a Hexadragon Fractal Use Cases
- Generative art and tiling patterns built from hexagonally symmetric fractal curves
- Classroom demonstrations of how turn angle and axiom shape change an L-system's overall layout independent of its production rule
- Downloadable SVG line art for design projects that want a hexagon-based fractal motif
Common Mistakes
- Expecting "hexadragon" to match a fixed formula from a math reference, this is a self-consistent construction we defined for this tool, not a term with one canonical definition.
- Confusing this with a plain terdragon curve, the underlying rule is identical but the turn angle (60 vs 120 degrees) and six-segment axiom are different, producing a very different overall shape.
Tips
- Compare against the Quaddragon Curve Generator to see how the same idea, a folding rule repeated N times around a center, changes shape with a different base rule and fold count.
- Zoom into the downloaded SVG in a vector editor to inspect how each of the six hexagon edges folds independently at high iteration counts.