Draw V Fractal

No. The classical Lévy C curve, introduced by Paul Lévy in 1938 (Les courbes planes ou gauches et les surfaces composées de parties semblables au tout), uses the L-system axiom F with rule F → +F–F+ – that is 2 F’s per substitution, not 5. The Lévy C curve is space-filling (dim 2.0). This tool’s 5-F rule produces a completely different figure with dim around 1.084. The name “Lévy C curve” was attached to this tool by mistake in the original docs and has been removed.

The honest box-counting dimension is log(5) divided by log(3 + √2), which works out to about 1.084. Derivation: one application of the rule F → F+F-F-F+F, starting at the origin heading up, traces 5 unit-length segments ending at (0, 3 + √2) ≈ (0, 4.414). So one F is replaced by 5 sub-F’s covering a diameter ratio of 4.414. The Moran-style similarity dimension is therefore log 5 / log 4.414 ≈ 1.084. An older version of the code returned log(5) / log(√2) ≈ 4.6438 – which is mathematically impossible in 2D (dim cannot exceed 2). An older version of the FAQ separately claimed “≈ 1.9340” – that figure has no clear derivation and may have been borrowed from a different fractal. Both old numbers were wrong; the current value reflects the actual geometry of this L-system.

Exactly 5 to the N. Iter 1 = 5; iter 4 = 625; iter 7 = 78,125. An older version of the spec said “iter 1 = 3 segments” – that contradicted the FAQ (which correctly said 5) and the code. The code has always produced 5ᴺ; the spec is now consistent.

Because the L-system stretches forward each iteration: the rule’s expansion covers 4.414 units while replacing what was 1 unit, so the curve elongates. With dim around 1.084 (only slightly above 1.0), the curve is almost line-like – it has thin “branches” rather than filling area densely.

Symmetry mode alternates indigo and cyan per consecutive segment, which visually pairs up left/right branches generated by the symmetric rule. Depth shading interpolates from the line color toward pink based on a running count of +/− turns (current recursion-depth proxy), so deeper branches appear in warmer color.

5 to the 7 = 78,125 segments. Iter 8 would be 390,625 – too slow for live exploration in a typical browser. Iter 7 is already at the edge; the tool gives a non-blocking time estimate before running it.

No. The tool loads three static files (HTML, CSS, JS) and then runs entirely in your browser – L-system expansion, drawing, PNG export, clipboard copy. You can disconnect from the internet after the page loads. No analytics, no tracking, no cookies.

Yes – free, unlimited, no signup, no watermark. Use the PNGs in lectures, papers, blog posts, or art freely. Attribution to is appreciated but not required.