# Koch curve generator

## World's simplest math tool

Free online fractal Koch curve generator. Just press a button and you'll automatically get a Koch snowflake. There are no ads, popups or nonsense, just an awesome Koch curve generator. Press a button, get a snowflake. Created by mathematicians for mathematicians.

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Koch curve generator tool
What is a Koch curve generator?

This tool draws Koch curves that look like snowflakes and stars. The Koch curve is one of the earliest known fractals. It's a typical geometric fractal that constructed by starting with an equilateral triangle, then recursively adding another equilateral triangle pointing outwrads in the middle of each side of the starting triangle. With a large number of such iterations the starting triangle becomes a snowflake. Because of its shape it's also known as Koch island. When using this tool to draw Koch fractals, you can select color inside and around snowflakes and also the color of the curve itself. You can set curve dimensions (width and height) and choose the thickness of the star. You can also change how many iterations to evolve the curve for. Mathabulous!

Koch curve generator examples
Click to use

Draw a Koch Star with a Thick Border

This example constructs a Koch curve with curve width of 20px. As there are just 3 iterations it looks like a star.

**Required options**

Width of the snowflake.

Height of the snowflake.

Number of Koch curve iterations.

Color around the star.

Color inside the star.

Star's border color.

Width of the border.

Add extra distance between the
fractal and the frame.

Generate a 4th Order Koch Curve

This example builds a Koch snowflake with 4 generations using white and blue color tones. Line width is set to 5px and padding is set to 10px.

**Required options**

Width of the snowflake.

Height of the snowflake.

Number of Koch curve iterations.

Color around the star.

Color inside the star.

Star's border color.

Width of the border.

Add extra distance between the
fractal and the frame.

Generate a Koch Island

This example uses dark-redish-brown background and yellow foreground to draw a fabulous looking fractal curve. Draws it on a 500x500 square with padding 10px using 5 iterations. As iterations increase the Koch curve starts to look like an island.

**Required options**

Width of the snowflake.

Height of the snowflake.

Number of Koch curve iterations.

Color around the star.

Color inside the star.

Star's border color.

Width of the border.

Add extra distance between the
fractal and the frame.

Pro tips
Master online math tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlinemathtools.com/generate-koch-snowflake?&width=300&height=300&iterations=3&background-color=%23f4cfff&inside-color=%23d49bfa&line-segment-color=%23540269&line-width=20&padding=20

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