# 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. Created by fractal fans from team Browserling. 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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Encode the Hilbert fractal as a string.

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Encode the Peano fractal as a string.

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Encode the Moore fractal as a string.

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Encode the Cantor set as a string.

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Encode the Heighway Dragon as a string.

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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.

Toothpick Fractal

Generate a toothpick sequence fractal.

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ASCII Fractal

Generate an ASCII fractal.

ANSI Fractal

Generate an ANSI fractal.

Unicode Fractal

Generate a Unicode fractal.

Braille Fractal

Generate a braille code fractal.

Draw a Pseudofractal

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

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.

Generate a Self-similar Image

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

Find Fractal Patterns in Text

Find fractal patterns in any given text.

Find Fractal Patterns in Numbers

Find fractal patterns in any given number.

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