Koch Snowflake Generator

Generate and visualize Koch snowflakes with adjustable depth, colors, and line width. The Koch snowflake is one of the earliest fractals to be described mathematically.

Controls

Depth: 3

Line Width: 1

Stroke Color

Fill interior

Background

Dark background

About Koch Snowflake

The Koch snowflake was first described by the Swedish mathematician Helge von Koch in 1904. It is constructed by starting with an equilateral triangle and recursively replacing the middle third of each line segment with two sides of a smaller equilateral triangle pointing outward.

Infinite perimeter, finite area: With each iteration, the perimeter grows by a factor of 4/3, approaching infinity. Yet the area converges to 8/5 of the original triangle.
Hausdorff dimension: log(4)/log(3) ≈ 1.2619, meaning it is more than a line but less than a plane.
Self-similarity: Every section of the snowflake boundary is a scaled copy of the whole boundary.
Historical significance: One of the earliest fractals described, predating the term "fractal" itself by decades.

Embed This Util

You can embed this util on your own site as a widget. Adding ?embed=1 to the URL loads a compact version with just the tool itself; no header, menu, or documentation. Paste this snippet into your HTML:

Copy snippet Adjust the height to taste.

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