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Hexaflake fractal

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. Fractabulous!
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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.
Hexaflake fractal tool What is a hexaflake fractal?
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 examples Click to use
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.
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).
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.
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 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-hexaflake-fractal?&width=500&height=500&iterations=3&form-1=true&background-color=white&line-segment-color=black&fill-color=%2372ff47&line-width=4&padding=15&direction=left
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