Multiflake fractal

World's simplest fractal tool

This utility lets you draw unique and colorful multiflake fractals. You can choose the number of sides of the initial regular polygon and set the number of subsequent fractal iterations. You can rotate the fractal, as well as adjust the size of the canvas, the thickness of the line that's used to draw polygons, and the padding around the canvas. You can use your own color palette to color the background, line, and interior of polygons. Fun fact – the boundary of the n-gon fractal is the Koch curve with an angle of 180 - α degrees, where α is the internal angle of the n-gon. Created by fractal fans from team Browserling. Fractabulous!

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multiflake fractal

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Multiflake fractal options

Edges, Depth, and Size

n-sided polygon Number of edges of the regular polygon. (Should be 5 or more.)

Iterations Multiflake's iterative depth.

Width Width.

Height Height.

Polyflake Colors

Background Multiflake background color.

Line color Multiflake border color.

Internal color Multiflake fill color.

Line, Padding and Orientation

Line Width Border line width.

Padding Extra pixels along image sides.

Direction Multiflake's orientation.

What is a multiflake fractal?

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This online browser-based tool allows you to illustrate the n-fold symmetry of multiflake fractals. A multiflake fractal is sometimes also called a polyflake fractal or just a polyflake for short. This fractal was first studied by a Polish mathematician Sierpinsky, who found the connection between the flakes and Koch curves. As the name suggests, a polyflake fractal starts with a regular n-sided polygon. Then, n copies of this polygon are created, each smaller by a factor proportional to n, and fit into the vertices of the original polygon. This leads us to the second iteration stage of the fractal. To perform the third iteration, we create n copies of the new pattern and repeat the process again. Thus, the number of n-gons at the i-th iteration step is equal to n^(i - 1). As the number of sides of the original flake increases, the fractal evolves to a circle with a massive empty center. In fact, a higher order multiflake contains infinitely many Koch curves, whose angle decreases with increasing values of n. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!

Multiflake fractal examples

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Sierpinski Heptagon

In this example, we generate a multiflake fractal with a regular heptagon in the base (hepta means seven). We evolve it for 4 iterations and get a heptagon fractal with 7^(4 - 1) = 343 heptagons. We use a givry color canvas of 600x600 pixels, a black line for the borders of heptagons and a persimmon color for heptagon fill. A heptagon multiflake is also called a Sierpinski Heptagon.

$In this example, we generate a multiflake fractal with a regular heptagon in the base (hepta means seven). We evolve it for 4 iterations and get a heptagon fractal with 7^(4 - 1) = 343 heptagons. We use a givry color canvas of 600x600 pixels, a black line for the borders of heptagons and a persimmon color for heptagon fill. A heptagon multiflake is also called a Sierpinski Heptagon.$

Required options

These options will be used automatically if you select this example.

n-sided polygon Number of edges of the regular polygon. (Should be 5 or more.)

Iterations Multiflake's iterative depth.

Width Width.

Height Height.

Background Multiflake background color.

Line color Multiflake border color.

Internal color Multiflake fill color.

Line Width Border line width.

Padding Extra pixels along image sides.

Direction Multiflake's orientation.

A Base 6 Multiflake

This example puts a regular 6-gon in the base, thus generating the well-known hexaflake fractal. It uses 5 iteration steps here and the image is composed of 6^(5 - 1) = 1296 hexagons. The hexagons are drawn without a border and are only filled with white color.

$This example puts a regular 6-gon in the base, thus generating the well-known hexaflake fractal. It uses 5 iteration steps here and the image is composed of 6^(5 - 1) = 1296 hexagons. The hexagons are drawn without a border and are only filled with white color.$

Required options

These options will be used automatically if you select this example.

n-sided polygon Number of edges of the regular polygon. (Should be 5 or more.)

Iterations Multiflake's iterative depth.

Width Width.

Height Height.

Background Multiflake background color.

Line color Multiflake border color.

Internal color Multiflake fill color.

Line Width Border line width.

Padding Extra pixels along image sides.

Direction Multiflake's orientation.

Decagon Necklace Fractal

In this example, we generate a decagon fractal (the base is a ten-sided polygon). As its internal angle is 144° degrees, the Koch curve around it has 180°-144° = 36° degrees. Because of its stunning symmetry, this fractal type is often used to design necklaces. If you count carefully, you'll find there are 10^(4 - 1) = 1000 decagons in this drawing. Decagons are drawn with black ink on a disco-red background and filled with a yellow color.

$In this example, we generate a decagon fractal (the base is a ten-sided polygon). As its internal angle is 144° degrees, the Koch curve around it has 180°-144° = 36° degrees. Because of its stunning symmetry, this fractal type is often used to design necklaces. If you count carefully, you'll find there are 10^(4 - 1) = 1000 decagons in this drawing. Decagons are drawn with black ink on a disco-red background and filled with a yellow color.$

Required options

These options will be used automatically if you select this example.

n-sided polygon Number of edges of the regular polygon. (Should be 5 or more.)

Iterations Multiflake's iterative depth.

Width Width.

Height Height.

Background Multiflake background color.

Line color Multiflake border color.

Internal color Multiflake fill color.

Line Width Border line width.

Padding Extra pixels along image sides.

Direction Multiflake's 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-multiflake-fractal?&width=600&height=600&iterations=4&polygon=7&background-color=%23F7E4BE&line-segment-color=black&fill-color=%23FF5656&line-width=5&padding=5&direction=up

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