# Pentaflake Fractal Generator

## 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!

Tool Options

#### Pentagon Options

Create a pentaflake from
five pentagons.
Create a pentaflake from
six pentagons with one
extra pentagon in the
center.
Create a pentaflake with
all centers filled with
pentagons.

#### Recursion and Dimensions

Recursive order of the fractal.
Canvas width
Canvas height
Pentaflake curve width.
Extra space around the curve.

#### Colors and Direction

Canvas fill color.
Pentaflake curve color.
Pentaflake fill color.
Pentaflake direction.

## What Is a Pentaflake Fractal Generator?

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 Generator Examples

Click to try!

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

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

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

### 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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