# Flowsnake fractal

## World's simplest fractal tool

This utility lets you draw the amazingly beautiful flowsnake fractals via a very simple and convenient interface. You can manage the fractal's generation process by changing a variety of settings, such as the number of iterations, color palette, drawing brush's thickness, fractal's direction, image size and its padding. Fun fact – asymptotically, the flowsnake curve fills the entire hexagon-like shape and forms a Gosper island. Fractabulous!

announcement
heads up!

We just launched a new site – Online Integer Tools – a collection of utilities for crunching integers. Check it out!

*fullscreen*

*fullscreen_exit*

A link to this tool, including input, options and all chained tools.

Can't convert.

Flowsnake fractal tool
What is a flowsnake fractal?

This online browser-based tool allows you to interactively illustrate flowsnake fractals. The flowsnake fractal creates a snake-like path that never crosses. The path of a flowsnake is constructed from a continuous line that at every couple of steps is always bent by 60 degrees. This fractal is also known as the Gosper curve. It's named after American mathematician and programmer Ralph William Gosper Jr. The famous mathematicians Mandelbrot and Gardner have also called it the Peano-Gosper curve as it has some similarity to the Peano fractal curve. It's also very similar to the Hilbert and Moore fractals as it's space-filling. However, unlike Peano, Hilbert and Moore fractals that fill a rectangle (or square) shaped space, the Peano-Gosper curve fills a space in the shape of a distorted hexagon. This distorted hexagon is called the Gosper island and seven of its copies can be joined together to form another larger copy of the island. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!

Flowsnake fractal examples
Click to use

Stage-three Flowsnake Fractal

This example displays the third stage of Peano-Gosper fractal. Stage three means that it has been iterated three times. This example uses a square canvas with a size of 900 by 900 pixels and padding of 20 pixels. It draws a white snake line with a thickness of 7 pixels on a pink background.

**Required options**

The number of recursive
repetitions (iterations.)

Fractal width.

Fractal height.

Pen's thickness for drawing
the fractal.

Pen's color for drawing
the fractal.

Fractal's background color.

Add padding around flowsnake.

Gosper Island

In this example, we create a Gosper island. The Gosper island is the final shape of the flowsnake fractal when the iterations count is large. In this case, it took 6 iterations to fully fill the hex-shape space that the flowsnake inherently occupies. Fun fact – Gosper island is a space-filling tile that can cover the entire plane. The colors used for drawing this fractal island are maroon-oak and lemon-chiffon.

**Required options**

The number of recursive
repetitions (iterations.)

Fractal width.

Fractal height.

Pen's thickness for drawing
the fractal.

Pen's color for drawing
the fractal.

Fractal's background color.

Add padding around flowsnake.

Stretched Flowsnake Curve

In this example, we've stretched the flowsnake fractal vertically with a ratio of 1.2. We're using a rectangular canvas with the width equal to 1000 pixels and the height equal to 1200 pixels.

**Required options**

The number of recursive
repetitions (iterations.)

Fractal width.

Fractal height.

Pen's thickness for drawing
the fractal.

Pen's color for drawing
the fractal.

Fractal's background color.

Add padding around flowsnake.

Pro tips
Master online fractal 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://onlinefractaltools.com/draw-flowsnake-fractal?&width=900&height=900&iterations=3&background-color=%23a6005b&line-segment-color=white&line-width=7&padding=20&direction=up

All fractal tools

Quickly draw a custom McWorter dendrite fractal.

Quickly draw a custom canopy tree fractal.

Quickly draw a custom Gosper fractal.

Quickly draw a custom Z-order fractal.

Quickly draw a custom Hilbert fractal.

Quickly draw a custom binary v-fractal.

Quickly draw a custom Peano fractal.

Quickly draw a custom Heighway dragon fractal.

Quickly draw a custom twin dragon Heighway fractal.

Quickly draw a custom Heighway nonadragon fractal.

Quickly draw a custom Koch fractal.

Quickly draw a custom triflake fractal.

Quickly draw a custom Sierpinski triangle fractal.

Quickly draw a custom Sierpinski pentagon fractal.

Quickly draw a custom Sierpinski hexagon fractal.

Quickly draw a custom Sierpinski polygon fractal.

Quickly draw a custom Moore fractal.

Quickly draw a custom Cantor comb fractal.

Quickly draw a custom Cantor dust fractal.

Quickly draw a custom Levy fractal curve.

Quickly draw a custom ice fractal.

Quickly draw a custom Pythagoras tree fractal.

Quickly draw a custom t-square fractal.

Quickly draw a custom Hausdorff tree fractal.

Coming soon
These fractal tools are on the way

Generate a Hilbert Sequence

Walk the Hilbert fractal and enumerate its coordinates.

Generate a Peano Sequence

Walk the Peano fractal and enumerate its coordinates.

Generate a Moore Sequence

Walk the Moore fractal and enumerate its coordinates.

Generate a Cantor String

Encode the Cantor set as a string.

Generate a Hilbert String

Encode the Hilbert fractal as a string.

Generate a Peano String

Encode the Peano fractal as a string.

Generate a Moore String

Encode the Moore fractal as a string.

Generate a Dragon String

Encode the Heighway Dragon as a string.

Generate a Sierpinski String

Encode the Sierpinski fractal as a string.

Mandelbrot Tree

Generate a Mandelbrot tree fractal.

Barnsey's Tree

Generate a Barnsley's tree fractal.

Barnsey's Fern

Generate a Barnsley's fern fractal.

Binary Fractal Tree

Generate a binary tree fractal.

Ternary Fractal Tree

Generate a ternary tree fractal.

Dragon Fractal Tree

Generate a dragon tree fractal.

De Rham Fractal

Generate a de Rham curve.

Takagi Fractal

Generate a Takagi-Landsberg fractal curve.

Peano Pentagon

Generate a Peano pentagon fractal curve.

Tridendrite Fractal

Generate a tridendrite fractal curve.

McWorter's Pentigree

Generate a Pentigree fractal curve.

McWorter's Lucky Seven

Generate a lucky seven fractal curve.

Eisenstein Fractions

Generate an Eisenstein fractions fractal curve.

Bagula Double V

Generate a Bagula double five fractal curve.

Julia Set

Generate a Julia fractal set.

Mandelbrot Set

Generate a Mandelbrot fractal set.

Toothpick Fractal

Generate a toothpick sequence fractal.

Ulam-Warburton Fractal

Generate an Ulam-Warburton fractal curve.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!