Is "polyflake" a standard, named fractal like the pentaflake or hexaflake?

No, and we want to be upfront about that. The pentaflake and hexaflake are well-documented fractals built on pentagon and hexagon bases. This tool generalizes the same center-plus-n-copies construction to a regular octagon base, a side count that doesn't have its own famous name in the literature, so "polyflake" here is our own extension of the pattern rather than a citation to an established fractal.

How is the octagon's scale factor chosen?

It uses a fixed scale factor tuned so the 8 surrounding octagons plus the center copy fit around the parent shape without excessive overlap, following the same center-plus-n-copies logic as the pentaflake and hexaflake, just applied to 8 sides instead of 5 or 6.

What does the Depth input control?

Depth sets how many recursive rounds are drawn, from 0 to 3. At depth 0 you get a single octagon. Each added level replaces every octagon from the previous level with 9 smaller octagons, 1 centered and 8 arranged around it.

Why is the maximum Depth lower than the pentaflake and hexaflake tools?

Each level here produces 9 child copies instead of 6 or 7, so the shape count grows faster with each level. Depth is capped at 3 to keep the individual octagons from shrinking past the point of being visible on the rendered canvas.

Sierpinski Polyflake Generator - Octagon n-flake SVG

Overview

Introduction

The pentaflake and hexaflake fractals both follow the same idea, a central polygon surrounded by scaled copies of itself. This tool applies that same idea to a regular octagon, a base shape that doesn't have its own established name in the n-flake literature.

We're building this honestly as our own generalization of a documented pattern to a new side count, not presenting it as a classical named fractal the way the pentaflake and hexaflake are.

What Is Generate a Sierpinski Polyflake?

A fractal made of a central regular octagon with 8 more octagons arranged around its edges, each one scaled down by a fixed factor. The same 9-copy pattern then repeats inside each of those octagons.

It's a direct extension of the n-flake construction used by the pentaflake (5 sides) and hexaflake (6 sides), generalized here to 8 sides.

How Generate a Sierpinski Polyflake Works

The tool starts with one regular octagon. At the first recursive step, it places 8 smaller octagons around the original's edges, each scaled down, plus one more copy at the same scale sitting on the original's center.

That gives 9 total sub-octagons per level, 8 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 9^depth resulting octagons drawn as a filled polygon.

When To Use Generate a Sierpinski Polyflake

Use it when you want an n-flake style fractal with 8-fold symmetry for generative art or visual exploration, and you're comfortable that this specific base polygon is our own extension rather than a textbook-named fractal.

If you specifically need a fractal with a documented mathematical name, use the pentagon-based Sierpinski Pentagon Generator or the hexagon-based Sierpinski Hexagon Generator instead.

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

Features

Advantages

Extends a well-understood construction (center-plus-n-copies) to a base polygon not commonly covered elsewhere.
8-fold symmetry gives a denser, more intricate look than the pentaflake or hexaflake at the same depth.
Filled-polygon rendering makes the recursive structure easy to read.

Limitations

Not a documented, named fractal, it's our own generalization of the n-flake pattern to an octagon base.
Depth is capped at 3, lower than the pentaflake/hexaflake tools, since 9 child copies per level grows the shape count faster.

Examples

Depth 2 polyflake

Input

Depth: 2

Output

A cluster of octagons showing 2 recursive levels of the 9-copy (1 center plus 8 surrounding) pattern, with visible 8-fold symmetry.

Each of the 9 octagons from depth 1 is replaced with its own scaled center-plus-8 arrangement.

Best Practices & Notes

Best Practices

Start at Depth 1 to see the base center-plus-8 arrangement clearly before moving to Depth 2 or 3.
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 = 8` and a fixed `scale = 0.34`, chosen to keep 8 surrounding octagons plus a center copy visually tight without excessive overlap. 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, mirroring the pentaflake/hexaflake recursion but generalized to 8 sides and a 9-copy branching factor. Depth is bounded to 0-3 by `boundsCheck`.

Generate a Sierpinski Polyflake Use Cases

Generative art exploring n-flake fractals beyond the classic pentagon and hexagon bases
Visual comparisons of how side count and branching factor change n-flake density
Design references needing an intricate, 8-fold symmetric geometric texture

Common Mistakes

Citing this as a named classical fractal like the pentaflake or hexaflake, it's our own extension of that construction to an octagon base.
Expecting the same Depth range as the pentaflake/hexaflake tools, this one tops out lower because each level produces more child copies.

Tips

Compare this tool against Sierpinski Hexagon Generator to see how increasing the side count from 6 to 8 changes the fractal's density at the same depth.
Keep Depth at 1 or 2 for design work where individual octagons need to stay visually distinct.

Generate a Sierpinski Polyflake