Hexaflake Fractal Generator

World's Simplest Fractal Tool

This utility lets you draw colorful and custom hexaflake fractals. You can change the fractal's appearance by selecting one of its three types (regular, partial or full hexaflake), adjusting the depth of iterations, setting the dimensions of the canvas, and choosing the color palette. You can customize hexagon fill color, outline color, and canvas color. Fun fact - the hexaflake fractal can be constructed by projecting the Cantor cube onto the plane orthogonal to its main diagonal. Created by fractal fans from team Browserling. Fractabulous!

Tool Options

Hexagon Options

Construct the hexaflake
fractal from six hexagons.
Draw the hexaflake with
a central seventh hexagon.
Draw the hexaflake with
hexagons placed in all
hexagon centers.

Iterations and Dimensions

Iteration depth of the fractal.
Width (px).
Height (px).
Hexaflake line width (px).
Padding around hexaflake (px).

Colors and Orientation

Canvas color.
Hexaflake line color.
Hexaflake fill color.
Hexaflake fractal
orientation.

What Is a Hexaflake Fractal Generator?

This online browser-based tool illustrates various types of Sierpinski hexaflake fractal. This fractal, often simply called a hexaflake for short, was first discovered by Waclaw Sierpinski, a Polish mathematician. One of the most important properties of the hexaflake fractal is its self-similarity. The Sierpinski hexaflake is formed from a single hexagon, which then has smaller copies of itself placed at its vertices so that they all touch but not overlap. In some variations of the fractal, the seventh hexagon can be placed in the center of all other touching hexagons. With each iteration, the size of hexagons decreases by ⅓. You can almost instantly see the self-similarity pattern in this pattern – the new flakes have the same shape, structure, proportions as the whole fractal, except that they are on a different scale. Besides its self-similarity, it also has 6-fold symmetry. Hexaflake's exterior boundary is the Koch snowflake and the full boundary contains an infinite number of Koch snowflakes. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!

Hexaflake Fractal Generator Examples

Click to try!

Hexaflake from Six Hexagons

In this example, we're creating the third stage hexaflake fractal from six hexagons. This hexaflake type omits the seventh hexagon from the center of the fractal. This fractal type is the original hexaflake that was studied by Sierpinski. We've also chosen the white for canvas, set its size to 500 by 500 pixels, adjusted the outline of hexagons to be 4 pixels wide and black color, and filled the hexagons with screaming-green color.

Required options
These options will be used automatically if you select this example.
Construct the hexaflake
fractal from six hexagons.
Iteration depth of the fractal.
Width (px).
Height (px).
Hexaflake line width (px).
Padding around hexaflake (px).
Canvas color.
Hexaflake line color.
Hexaflake fill color.
Hexaflake fractal
orientation.

Partial Hexaflake Fractal

In this example, we're generating the partial hexaflake type. This type puts another hexagon in the center of all hexagons. It's called partial type because unlike full hexaflake (see next example) it only uses one extra hexagon. The hexagons in this example have a yellow border, which is 5 pixels thick and it's drawn on a resolution-blue background. We're also using rectangular space size of 600 by 700 pixels and adjusting the fractal orientation to up (which actually rotates fractal by 30 degrees).

Required options
These options will be used automatically if you select this example.
Draw the hexaflake with
a central seventh hexagon.
Iteration depth of the fractal.
Width (px).
Height (px).
Hexaflake line width (px).
Padding around hexaflake (px).
Canvas color.
Hexaflake line color.
Hexaflake fill color.
Hexaflake fractal
orientation.

Full Hexaflake Fractal

This example generates the third type of hexaflake, which is the full hexaflake fractal. The key difference between the partial and full hexaflake is that the full hexaflake puts a hexagon in the center of every available hexagon (not just center as partial one). We've left hexagon outline color and width options empty and this fractal uses only two color palette – claret color for hexagons and a sweet-corn color the canvas.

Required options
These options will be used automatically if you select this example.
Draw the hexaflake with
hexagons placed in all
hexagon centers.
Iteration depth of the fractal.
Width (px).
Height (px).
Hexaflake line width (px).
Padding around hexaflake (px).
Canvas color.
Hexaflake line color.
Hexaflake fill color.
Hexaflake fractal
orientation.

Pro tipsMaster 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!

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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 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 Cantor String

Encode the Cantor set 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.

Sierpinski Pyramid

Generate a Sierpinski tetrahedron (tetrix) fractal.

Cantor's Cube

Generate a Cantor's cube fractal.

Menger Sponge

Generate a Sierpinski-Menger fractal.

Jerusalem Cube

Generate a Jerusalem cube fractal.

Mosely Snowflake

Generate a Jeaninne Mosely fractal.

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.

Mandelbulb Fractal

Generate a Mandelbulb fractal.

Mandelbox Fractal

Generate a Mandelbox fractal.

Buddhabrot Fractal

Generate a Buddhabrot fractal.

Burning Ship Fractal

Generate a Burning Ship fractal.

Toothpick Fractal

Generate a toothpick sequence fractal.

Ulam-Warburton Fractal

Generate an Ulam-Warburton fractal curve.

ASCII Fractal

Generate an ASCII fractal.

ANSI Fractal

Generate an ANSI fractal.

Unicode Fractal

Generate a Unicode fractal.

Emoji Fractal

Generate an emoji fractal.

Braille Fractal

Generate a braille code fractal.

Audio Fractal

Generate a fractal in audio form.

Draw a Pseudofractal

Create a fractal that looks like one but isn't a fractal.

Convert Text to a Fractal

Generate a fractal from any text.

Convert a String to a Fractal

Generate a fractal from a string.

Convert a Number to a Fractal

Generate a fractal from a number.

Merge Two Fractals

Join any two fractals together.

Draw a Random Fractal

Create a completely random fractal.

Iterate an IFS

Set up an arbitrary IFS system and iterate it.

Run IFS on an Image

Recursively transform an image using IFS rules.

Iterate an ICAF

Run infinite compositions of analytic functions.

Generate a Fractal Landscape

Create a surface that mimics a natural terrain.

Generate a Brownian Surface

Create a fractal surface via Brownian motion.

Generate a Self-similar Image

Apply fractal algorithms on your image and make it self-similar.

Find Fractal Patterns in Images

Find fractal patterns in any given image.

Find Fractal Patterns in Text

Find fractal patterns in any given text.

Find Fractal Patterns in Numbers

Find fractal patterns in any given number.

Fill a Plane with Fractals

Tessellate a plane with fractals.

Run a Cellular Automaton

Run a cellular automaton with custom rules.

Play Game of Life

Play Conway's Game of Life on an infinite grid.

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