Is the Triflake Curve a single classical fractal?

No, and we want to be upfront about that. It's a composite we build from a completely standard curve, the Koch Star snowflake, drawn three times with the second and third copies each rotated 120 degrees around the same center point. The Koch Star itself is textbook fractal geometry, the tri-fold overlap arrangement is our own construction on top of it.

Why three copies at 120 degrees specifically?

120 degrees divides a full rotation into three equal parts, so three copies of the same snowflake, spaced evenly, produce a symmetric rosette rather than a lopsided overlap. It's the natural spacing for combining three identical shapes around one center.

Are the three snowflakes actually merged into one curve?

No, each of the three Koch Star copies is a separate closed curve computed independently, then rotated and drawn on top of the others in the same SVG. They overlap visually to form the rosette, but they're not merged into a single connected path, so where they cross, you're seeing three curves layered, not a new combined outline.

How does the Iterations control affect the rosette?

It sets the iteration depth of each of the three underlying Koch Star curves before they're rotated and overlaid, so higher values make every one of the three snowflakes more jagged and detailed, which in turn makes the overlapping rosette pattern denser.

Triflake Curve Generator - Three Rotated Koch Snowflakes Online

Overview

Introduction

A single Koch Star snowflake is a well-known, symmetric fractal on its own. This tool takes that same snowflake and draws it three times, rotating each additional copy 120 degrees around a shared center, so the three overlap into a denser, tri-fold rosette pattern.

Set an iteration count and the tool renders the composite as an SVG line drawing, downloadable as SVG or PNG.

What Is Generate a Triflake Curve?

A generator that overlays three copies of the Koch Star snowflake curve, rotated 120 degrees apart around one shared center point, into a single rosette-like composite image. The underlying snowflake is a genuine classical fractal, the three-way rotated overlay is our own composite construction, built for this catalog rather than a textbook-documented single curve.

The output is three overlapping unfilled outlines rendered together as stroked SVG paths.

How Generate a Triflake Curve Works

The tool first computes one Koch Star curve, a closed triangle base with the standard 60 degree Koch bump rule applied to all three sides, at the requested iteration depth.

That curve is then drawn three times: once unrotated, once rotated 120 degrees around the shared center, and once rotated 240 degrees, using simple 2D rotation of every point in the curve's coordinate list.

All three rotated copies are combined into one set of path segments and rendered together in a single SVG, so the overlapping regions show where the three snowflakes cross rather than being merged into one new outline.

When To Use Generate a Triflake Curve

Use it when you want a denser, symmetric rosette pattern built from a recognizable snowflake shape, for decorative or pattern-design purposes.

It's also a good illustration of how simple rotation and overlay can turn one classical fractal into a more elaborate composite without changing the underlying curve math.

Often used alongside Generate a Koch Triangle, Generate a Cesaro Polyflake and Generate a Quadratic Cross Fractal.

Features

Advantages

Produces a visually rich, three-fold symmetric composite from a single well-understood base curve.
Each of the three underlying snowflakes uses exactly the same construction, so the rosette stays perfectly balanced at every iteration.
Downloadable as scalable SVG or a flattened PNG.

Limitations

Not a single classical fractal curve, it's a three-way rotated overlay we built on top of the standard Koch Star, and we label it as such rather than as an established named fractal.
The three copies are drawn as separate overlapping outlines, not merged into one connected boundary, so the crossing points aren't a new traceable path.

Examples

Iteration 0

Input

Iterations = 0

Output

Three plain triangle outlines, each rotated 120 degrees from the last, overlapping into a simple hexagram-like pattern.

At zero iterations each underlying Koch Star is just its base triangle, so the composite is three overlapping triangles.

Iteration 3 (default)

Input

Iterations = 3

Output

Three detailed Koch snowflakes, rotated 120 degrees apart, overlapping into a dense six-pointed rosette.

Each of the three underlying snowflakes has the Koch bump rule applied three times before rotation and overlay.

Best Practices & Notes

Best Practices

View iteration 0 or 1 first to see the three-way rotation structure clearly before moving to denser, more detailed levels.
Use the SVG download if you plan to recolor individual overlapping regions in a vector editor, PNG for a quick raster embed.

Developer Notes

The base curve reuses the Koch Star L-system preset, axiom `F++F++F` with rule `F -> F-F++F-F` at a 60 degree turn angle. Each of the three copies is produced by applying a standard 2D rotation matrix, `x' = x*cos(theta) - y*sin(theta)`, `y' = x*sin(theta) + y*cos(theta)`, at theta = 0, 120, and 240 degrees, to every segment endpoint before all three segment sets are merged and normalized together.

Generate a Triflake Curve Use Cases

Generating a symmetric rosette or mandala-style decorative pattern from a classical fractal
Illustrating how rotation and overlay can compose new visual structures from a single well-known curve
Producing a downloadable SVG asset for pattern or textile design work

Common Mistakes

Citing this as a single named classical fractal, it's our own three-way rotated composite built from the standard Koch Star curve.
Expecting the overlapping regions to form one new traceable outline, the three snowflakes remain separate curves drawn on top of each other.

Tips

Compare this against Koch Triangle Generator to see the single open curve that the underlying closed Koch Star (and in turn this rosette) is built from.
Try lower iteration counts first, the three-way rotation symmetry is easiest to see before the curves get visually dense.

Generate a Triflake Curve