Generate a Sierpinski Pentagon
Draw a Sierpinski pentaflake fractal. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate a Sierpinski Pentagon
- 1. Set the recursion depth. Choose Depth for how many times each pentagon splits into smaller pentagons around its edges. A depth-3 pentaflake already contains 216 filled pentagons.
- 2. Decide whether to fill the center. Toggle Include center pentagon to add or remove the middle pentagon from each subdivision, changing the overall density of the resulting pattern.
- 3. Size and style the drawing. Set Width (px), Height (px), Line color, Background color and Line width to fit the pentaflake's five-fold symmetric silhouette.
- 4. Review the rendered pentaflake. The tool draws the Sierpinski pentagon, or pentaflake, as an SVG of filled pentagons arranged in a five-fold symmetric pattern. Save it once the depth and center option look right.
When to use Generate a Sierpinski Pentagon
Generate a Sierpinski Pentagon draws the pentaflake, a five-fold symmetric fractal built by surrounding a pentagon with smaller copies of itself. Since regular pentagons cannot tile a plane without gaps, the pentaflake construction inherently leaves visible spaces between the pentagons at every level.
- Teaching why pentagons cannot tile a plane. The gaps visible in the pentaflake at every scale are a direct visual consequence of the fact that regular pentagons cannot tessellate, making this a good companion to a tiling lesson.
- Comparing five-fold symmetry to other polyflakes. Render the pentaflake next to the hexaflake and a general polyflake at the same depth to show how the number of sides changes both the symmetry and the amount of visible gap.
- Designing a five-pointed decorative motif. The pentaflake's five-fold symmetry and natural gaps give it a star-like, ornamental look suited to a badge, rosette or decorative border design.
- Illustrating self-similar structures with imperfect tiling. A geometry lesson on self-similarity can use the pentaflake to show that fractal recursion still works cleanly even when the base shape cannot perfectly tile the plane.
Examples
A depth-3 pentaflake
Output
An SVG drawing of the pentaflake made of 216 filled pentagons.
About the Generate a Sierpinski Pentagon tool
Generate a Sierpinski Pentagon does its work locally, right in the browser. Draw a Sierpinski pentaflake fractal. There is no upload step, no queue and no account, and your data never travels over the network.
It belongs to the Math Tools collection on EditSafely, a set of 234 small, focused Math utilities that share the same instant, private workspace.
You can shape the output with 7 settings, including Depth, Include center pentagon, Width (px) and Height (px), and the result refreshes the moment you change one. A worked example further down the page shows exactly what the tool produces for a real input.
Running locally also makes the tool fast and dependable: results appear as you type or drop a file, there is no server outage that can take it down mid-task, and confidential data can be processed without a second thought.
Frequently asked questions
Is Generate a Sierpinski Pentagon free to use?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
Everything happens locally. Your browser downloads the tool's code once, then does all the processing itself; nothing you enter is transmitted, stored or logged. You can even go offline after the page loads and it will still work.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
No. The tool works in any modern browser on desktop, tablet or phone. There is no account to create, no extension to add and no software to install.
Can I save what the tool produces?
Yes. Use the download or copy controls in the output panel to keep the rendered result once it looks the way you want.