# Pentaflake fractal

## World's simplest fractal tool

This utility lets you draw colorful and custom pentaflake fractals. You can choose between three different forms of this fractal – regular pentaflake, partial pentaflake, and full pantaflake. You can also set the fractal's recursive order, its size (width and height) in pixels, curve width and padding. To create the most beautiful fractal, you can customize colors for the background, curve, and inner fill. Fun fact – the boundary of a pentaflake is the Koch curve of 72 degrees. Fractabulous!

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Pentaflake fractal tool
What is a pentaflake fractal?

This online browser-based tool allows you to illustrate three primary types of Sierpinski pentaflake fractal. The pentaflake is a fractal with 5-fold symmetry and just like other flake fractals, it's self-similar. This fractal was first mentioned by Albrecht Durer but it was extensively studied by a Polish scientist Waclaw Sierpinski. To make a pentaflake, you first start with a pentagon and in every next recursive step, you place five identical (but smaller by a factor of 1/(1+φ), where φ is the golden ratio) pentagons at all vertices of the original pentagon. All further iteration steps are drawn in the same way. Self-similarity of this construction is instantly obvious as the pentagons in the next iteration have a smaller scale but have the same pattern and form as the whole fractal. The perimeter of a pentaflake can be approximated with multiple Koch curves that are bent and joined together. As the length of a Koch curve is infinite, so is the length of the perimeter of a pentаflake. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!

Pentaflake fractal examples
Click to use

Pentaflake with 25 Flakes

In this example, we select five pentagons as the base figure for the Sierpinski pentaflake. This fractal type starts with 1 pentagon at the 1st iteration step, at the second iteration step there are 5 pentagons, at the third – 25 (5×5), at the fourth – 125 (5×5×5). At the n-th step, there are 5^(n-1) pentagons. We display the third iteration step, which has 25 pentagons all connected vertex-to-vertex. We paint them in harlequin-green color, add a black 4px border around them, and fill the background with klein-blue color.

**Required options**

Create a pentaflake from
five pentagons.

Recursive order of the fractal.

Canvas width

Canvas height

Pentaflake curve width.

Extra space around the curve.

Canvas fill color.

Pentaflake curve color.

Pentaflake fill color.

Partial Pentaflake Fractal

In this example, we generate a partial Sierpinski pentaflake. The word partial here means it's not fully filled but just partially with an extra pentagon recursively placed in the middle of the original five pentagons. In this type of fractal, the number of pentagons increases as follows: 1 → 6 → 6×5 → 6×5×5 → … → 6×5^(n-2). We draw the fractal at a recursive depth of 4, so there are 150 pentagons in this drawing. We've also turned the pentaflake upside down. The canvas is set to a square of 700×700 pixels in size, the line is 5 pixels and padding is 20 pixels.

**Required options**

Create a pentaflake from
six pentagons with one
extra pentagon in the
center.

Recursive order of the fractal.

Canvas width

Canvas height

Pentaflake curve width.

Extra space around the curve.

Canvas fill color.

Pentaflake curve color.

Pentaflake fill color.

Durer Pentagon Fractal

In this example, we generate a Durer fractal. The Durer fractal is the third type of the pentaflake fractal, which completely fills all centers with extra pentagons. Here, with each iteration, the number of pentagons increases sixfold – there are five pentagons at the edges and one in the center. Thus, the number of pentagons at the nth iteration is equal to 6^(n-1). We illustrate the 5th iteration of the fractal and use only two colors, filling the pentagons with daisy color and background with comet color.

**Required options**

Create a pentaflake with
all centers filled with
pentagons.

Recursive order of the fractal.

Canvas width

Canvas height

Pentaflake curve width.

Extra space around the curve.

Canvas fill color.

Pentaflake curve color.

Pentaflake fill color.

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-pentaflake-fractal?&width=500&height=500&iterations=3&form-1=true&background-color=%23042fa6&line-segment-color=black&fill-color=%2328ff02&line-width=4&padding=15&direction=up

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Coming soon
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Generate a toothpick sequence fractal.

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