Is the hexaflake a real, documented fractal?

Yes. The hexaflake is a standard fractal construction, a central regular hexagon surrounded by 6 more hexagons, each scaled down by exactly 1/3. It's part of the same n-flake family as the pentaflake, just built on a hexagon base with a simpler scale factor.

Why is the scale factor exactly 1/3 instead of some other ratio?

A regular hexagon tiles neatly with copies of itself scaled by 1/3 placed around its perimeter and one more at the same scale in the center, so the 7-copies-per-level structure fits together with no gaps or overlap beyond the shared edges, which is what makes 1/3 the natural ratio for this construction.

What does the Depth input control?

Depth sets how many recursive rounds are drawn, from 0 to 4. At depth 0 you get a single hexagon. Each added level replaces every hexagon from the previous level with 7 smaller hexagons, 1 centered and 6 arranged around it, each at one third the previous scale.

How does this differ from the Sierpinski Pentagon Generator?

Both are n-flake constructions, a center copy plus n copies around it, but the pentaflake uses 5 surrounding pentagons at a golden-ratio-derived scale, while the hexaflake uses 6 surrounding hexagons at an exact 1/3 scale, giving each fractal a different symmetry and density.

Sierpinski Hexagon Generator

Overview

Introduction

The hexaflake extends the same n-flake idea behind the pentaflake to a hexagon base, a central hexagon with 6 more arranged around it, each scaled down by exactly one third.

It's a real, well-documented fractal, closely related to the Sierpinski triangle and carpet in spirit, subdivide and repeat, but built from hexagonal tiling instead of triangular or square grids.

What Is Generate a Sierpinski Hexagon?

A fractal made of a central regular hexagon with 6 more hexagons arranged around its edges, each one exactly a third the size of its parent. The same 7-copy pattern then repeats inside each of those hexagons.

It's one of the most commonly cited n-flake fractals, alongside the pentaflake, because the hexagon's natural 1/3 scale factor produces a clean, edge-to-edge tiling with no visible gaps.

How Generate a Sierpinski Hexagon Works

The tool starts with one regular hexagon. At the first recursive step, it places 6 smaller hexagons around the original's edges, each scaled by 1/3, plus one more copy at the same 1/3 scale sitting on the original's center.

That gives 7 total sub-hexagons per level, 6 arranged around the perimeter and 1 in the center, each one eligible for the same subdivision at the next level.

This repeats down to the chosen Depth, with every one of the 7^depth resulting hexagons drawn as a filled polygon.

When To Use Generate a Sierpinski Hexagon

Use it whenever you want an accurate hexaflake for math visualizations, generative art, or educational material about n-flake fractals and hexagonal tiling.

If you want the same idea on a different base polygon, see the pentagon-based Sierpinski Pentagon Generator or the octagon-based Sierpinski Polyflake Generator.

Often used alongside Generate a Sierpinski Pentagon, Generate a Sierpinski Polyflake and Generate a Sierpinski Square.

Features

Advantages

Implements the standard, mathematically exact hexaflake construction with a clean 1/3 scale factor.
The hexagon's natural tiling gives a visually dense but orderly result even at moderate depth.
Filled-polygon rendering makes the 6-fold symmetry clear at a glance.

Limitations

Depth is capped at 4, since the hexagon count grows by a factor of 7 per level and quickly produces a very large number of tiny shapes.
Only the standard 1/3 scale factor is offered, there's no option to use a different packing ratio.

Examples

Depth 3 hexaflake

Input

Depth: 3

Output

A dense, honeycomb-like cluster of hexagons showing 3 recursive levels of the 7-copy (1 center plus 6 surrounding) hexaflake pattern.

Each of the 7 hexagons from depth 2 is replaced with its own scaled center-plus-6 arrangement.

Best Practices & Notes

Best Practices

Start at Depth 2 to see the 6-fold symmetry and honeycomb-like tiling clearly before increasing further.
Use the SVG export for print or further vector editing, since the polygon points stay exact at any zoom level.

Developer Notes

Generated by the shared `nFlake(sides, scale, depth, radius, cx, cy, level, out)` helper with `sides = 6` and `scale = 1 / 3`. At each level the helper places `sides` child copies around the perimeter at `distance = radius * (1 - scale)` plus one more child copy centered on the same point, giving the standard 7-copies-per-level hexaflake recursion. Depth is bounded to 0-4 by `boundsCheck`.

Generate a Sierpinski Hexagon Use Cases

Math and geometry visualizations demonstrating n-flake fractals and hexagonal tiling
Generative art with a honeycomb-like, 6-fold symmetric texture
Educational material comparing hexaflake, pentaflake, and other n-flake constructions side by side

Common Mistakes

Assuming the hexaflake uses the same golden-ratio scale factor as the pentaflake, it doesn't, the hexagon's natural ratio is an exact 1/3.
Pushing Depth to the maximum immediately, at depth 4 the hexagon count is large enough that individual shapes become very small on screen.

Tips

Compare this tool with Sierpinski Pentagon Generator to see how the base polygon's shape changes the fractal's symmetry and density.
Zoom into the exported SVG to inspect the self-similar center-plus-6 structure at each level individually.

Generate a Sierpinski Hexagon