# Koch polyflake generator

## World's simplest math tool

Free online Koch polygon fractal generator. Just press a button and you'll get a Koch polyflake. There are no ads, popups or nonsense, just an awesome Koch flake generator. Press a button – get a Koch polyflake. Created by mathematicians for mathematicians.

love fractals?
check out fracal tools!

We just started working on Online Fractal Tools — utilities for doing fractaly things. Check it out!

A link to this tool, including input, options and all chained tools.

Can't convert.

Koch polyflake generator tool
What is a koch polyflake generator?

This tool generates Koch polyflake fractals. A Koch polyflake is also known as a Koch polygon, Koch n-gon, and Koch n-flake. This fractal originates from the Koch triangle and it generalizes this fractal to any polygon. In the case of Koch triangle, each side of the triangle is replaced by a three-segment zigzag. With Koch n-gon, we are expanding your opportunities here. In particular, you can now select the base polygon of the fractal, as well as change the angle at which zigzag is bent. Furthermore, you can generate any number of iterations of this fractal and adjust the final size of the fractal. To make it more pretty, you can highlight three areas of the Koch polyflake in different colors – you can change the background color, the zigzag line color, and the fill color of the fractal. Last but not least, you can also adjust pixel width of the zigzag line and how much free space to leave between fractal and the drawing frame. And for the kicks, we threw in an option that lets you rotate the Koch n-gon around its center axis. Mathabulous!

Koch polyflake generator examples
Click to use

Koch Hexagon

This example draws the Koch fractal from an equilateral 6-gon. The angle between the zigzag segments is 111 degrees. As we are generating 10 iterations of the fractal, the zigzag lines get so tiny and so close together that they delineate fractal's sharp, continuous edge.

**Required options**

Koch polygon's width.

Koch polygon's height.

Koch polygon's iterations.

Number of base polygon's sides.

Bend angle of zigzag segments.

Background color for
Koch's polyflake.

Koch polyflake's zigzag color.

Koch polyflake's fill color.

Koch polygon's border width.

Padding around Koch's polygon.

Heighway Triangle

In this example we bend the zigzag line at 120 degrees. To our surprise, we get the Heighway triangle fractal. To show more possibilities of this tool, we've made zigzag's width equal to zero, set the background to black color and triangle fill color to white, changed fractal's size to a 500x400px rectangle with 5-pixel indentation along the edges of the frame.

**Required options**

Koch polygon's width.

Koch polygon's height.

Koch polygon's iterations.

Number of base polygon's sides.

Bend angle of zigzag segments.

Background color for
Koch's polyflake.

Koch polyflake's zigzag color.

Koch polyflake's fill color.

Koch polygon's border width.

Padding around Koch's polygon.

Koch Heptagon

Here we've set the zigzag angle to the same as in the previous example (120 degrees) but because we take the heptagon (7-sided figure) as the basis for the fractal, we get something super interesting. The center shape that results has a solid fill but along the edges there are Heighway's triangles! We use bright colors to highlight each part of the fractal and generate seven iteration steps on a 500-pixel square canvas.

**Required options**

Koch polygon's width.

Koch polygon's height.

Koch polygon's iterations.

Number of base polygon's sides.

Bend angle of zigzag segments.

Background color for
Koch's polyflake.

Koch polyflake's zigzag color.

Koch polyflake's fill color.

Koch polygon's border width.

Padding around Koch's polygon.

Hexadragon Curve

In this example zigzag's angle is also 120 degrees, but here we disable fractal's fill color and get a hexadragon curve where dragons are connected heads to tails. These dragons are formed from Heighway's triangles, which you can see by reducing the number of iterations in the options.

**Required options**

Koch polygon's width.

Koch polygon's height.

Koch polygon's iterations.

Number of base polygon's sides.

Bend angle of zigzag segments.

Background color for
Koch's polyflake.

Koch polyflake's zigzag color.

Koch polyflake's fill color.

Koch polygon's border width.

Padding around Koch's polygon.

Koch Triangle

This example creates a Koch triangle fractal. As the title suggests, the base figure is a regular triangle and its sides are replaced with a zigzag made out of three equal-length parts that are cut at 108 degrees. We don't draw zigzag lines themselves and our fractal is drawn in yellow on a black background.

**Required options**

Koch polygon's width.

Koch polygon's height.

Koch polygon's iterations.

Number of base polygon's sides.

Bend angle of zigzag segments.

Background color for
Koch's polyflake.

Koch polyflake's zigzag color.

Koch polyflake's fill color.

Koch polygon's border width.

Padding around Koch's polygon.

Pro tips
Master online math 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://onlinemathtools.com/generate-koch-polyflake?&width=500&height=500&iterations=10&polygon=6&background-color=%232adde3&line-segment-color=black&fill-color=%23ff6ee9&angle=111&line-width=1&padding=3&direction=left

All math tools

Quickly visualize rules of an Lindenmayer rewrite system.

Quickly generate a list of primes.

Quickly generate a list of Fibonacci numbers.

Quickly generate a list of extended, negative Fibonacci numbers.

Quickly generate a list of Fibonacci primes.

Quickly generate a list of Fibonacci words.

Quickly generate a list of Tribonacci words.

Quickly generate a list of Lucas numbers.

Quickly generate a list of extended, negative Lucas numbers.

Quickly generate a list of Lucas numbers that are also prime numbers.

Quickly create a list of excessive numbers.

Quickly create a list of deficient numbers.

Quickly generate a list of perfect numbers.

Quickly create a list of slightly defective numbers.

Quickly generate random numbers.

Quickly generate a list of look-and-say sequence numbers.

Quickly create a list of Prouhet-Thue-Morse sequence values.

Quickly create a list of dragon curve sequence values.

Quickly create a list of Oldenburger-Kolakoski sequence values.

Quickly create a list of Gijswijt sequence values.

Quickly create a list of Golay-Rudin-Shapiro sequence values.

Quickly create a list of Baum-Sweet sequence values.

Quickly create a list of Moser-de Bruijn sequence values.

Quickly generate a list of even numbers.

Quickly generate a list of odd numbers.

Quickly find all factors of the given integer.

Quickly decompose integers into their prime factors.

Quickly find out if the given integer is a prime number.

Quickly check if the given number is a Fibonacci number

Quickly generate π constant's digits to arbitrary precision.

Quickly calculate Euler constant's digits to arbitrary precision.

Quickly calculate φ constant's digits to arbitrary precision.

Quickly calculate factorials.

Quickly create a triangluar array of binomial coefficients.

Quickly create a matrix with random elements.

Quickly create a unit matrix with ones along the diagonal.

Quickly find the transpose of a matrix.

Quickly find the inverse of a matrix.

Quickly calculate the determinant of a matrix.

Quickly find the sum of two or more matrices.

Find the difference of two or more matrices.

Quickly find the product of matrices.

Quickly draw a Hilbert space-filling curve.

Quickly draw a Heighway triangle fractal.

Quickly draw a Harter-Heighway space-filling dragon fractal.

Quickly draw a Davis-Knuth dragon fractal.

Quickly draw a triple dragon fractal.

Quickly draw a quaddragon fractal.

Quickly draw a hexdragon curve.

Quickly draw a Peano space-filling fractal.

Quickly draw a Moore space-filling curve.

Quickly draw a Peano-Gosper space-filling curve.

Quickly draw a Sierpinski arrowhead fractal curve.

Quickly draw a Sierpinski sieve fractal.

Quickly draw a Sierpinski closed plane fractal curve.

Quickly draw a Sierpinski carpet fractal.

Quickly draw a Sierpinski maze fractal.

Quickly draw a Sierpinski square fractal.

Quickly draw a Sierpinski pentaflake fractal.

Quickly draw a Sierpinski hexaflake fractal.

Quickly draw a Sierpinski n-gon fractal.

Quickly draw a Koch island fractal curve.

Quickly draw a Koch antisnowflake fractal.

Quickly draw a Koch triangle fractal.

Quickly draw a Koch n-gon fractal.

Quickly draw a quadratic Koch flake fractal.

Quickly draw a Cesaro fractal.

Quickly draw a Cesaro n-gon fractal.

Quickly draw a triflake fractal.

Quickly draw a quadric cross fractal.

Quickly draw a self-similar Levy C fractal curve.

Quickly draw a Vicsek snowflake fractal.

Quickly draw a T-square fractal.

Quickly draw a Cantor set fractal.

Quickly draw an asymmetric Cantor set fractal.

Quickly draw a generalized Cantor set fractal.

Quickly draw an ε-Cantor set fractal.

Quickly draw a Cantor dust fractal.

Quickly draw a Pythagoras tree fractal.

Quickly draw a Fibonacci word fractal.

Quickly draw an H-tree fractal.

Quickly draw a V-tree fractal.

Quickly generate a Morton Z-order fractal curve.

Coming soon
These math tools are on the way

Find n-th e Digit

Calculate the n-th digit of Euler's number.

Find n-th Golden Ratio Digit

Calculate the n-th digit of Golden Ratio.

Find n-th Pi Digit

Calculate the n-th digit of pi constant.

Decode a Look-and-say Sequence

Perform the inverse operation on a look-and-say sequence.

Generate Stanley Number Sequence

Create a list of Stanley numbers.

Generate Bell Number Sequence

Create a list of Bell numbers.

Generate Carmichael Number Sequence

Create a list of Charmichel numbers.

Generate Catalan Number Sequence

Create a list of Catalan numbers.

Generate Composite Number Sequence

Create a list of composite numbers.

Generate Secant Number Sequence

Create a list of secant numbers.

Generate Golomb Number Sequence

Create a list of Golomb-Silverman numbers.

Generate Euler's Totient Number Sequence

Create a list of Euler's phi numbers.

Generate Juggler Number Sequence

Create a list of juggler numbers.

Generate Lucky Number Sequence

Create a list of lucky numbers.

Generate Motzkin Number Sequence

Create a list of motzkin numbers.

Generate Padovan Number Sequence

Create a list of Padovan numbers.

Generate Pseudoperfect Number Sequence

Create a list of semiperfect numbers.

Generate Ulam Number Sequence

Create a list of Ulam numbers.

Generate Weird Number Sequence

Create a list of weird numbers.

Generate Superperfect Number Sequence

Create a list of superperfect numbers.

Partition a Number

Find all partitions of the given integer.

Generate Partition Number Sequence

Create a list of Partition function numbers.

Generate Arithmetic Progression

Create an arithmetic sequence of numbers.

Generate Geometric Progression

Create a geometric sequence of numbers.

Generate Natural Number Sequence

Create a list of natural numbers.

Generate Powers of Two

Create a list of numbers of powers of two.

Generate Powers of Ten

Create a list of numbers of powers of ten.

Multiply a Matrix by a Scalar

Multiply all matrix elements by a number.

Check if a Matrix is Singular

Determine if a matrix is degenerate.

Find the Co-factor Matrix

Given a matrix, find its cofactor matrix.

Find the Adjugate Matrix

Given a matrix, find its adjunct.

LU Factor a Matrix

Decompose a matrix into LU factors.

Find Matrix Eigenvalues

Find eigenvalues of a matrix.

Prettify a Matrix

Beautify a matrix by neatly aligning all its columns.

Reformat a Matrix

Convert matrix in one format to another format.

Draw a Fibonacci Spiral

Generate a Fibonacci spiral curve.

Draw Fibonacci Rectangles

Generate a drawing of Fibonacci rectangles.

Draw a Fibonacci Seed Head

Generate a Fibonacci flower head.

Draw a Padovan Fractal

Generate a Padovan equiliteral triangles fractal.

Draw a Apollonian Gasket

Generate an Apollonian gasket fractal.

Draw a Mandelbrot Fractal

Generate a Mandelbrot fractal.

Draw a Julia Fractal

Generate a Julia fractal.

Draw a Rauzy Fractal

Generate a Rauzy fractal.

Draw Blancmange Fractal Curve

Generate a Blancmange fractal.

Draw Weierstrass Function

Generate a Weierstrass fractal.

Draw Minkowski Question-mark Curve

Generate a Minkowski Question-mark fractal.

Draw Thomae's Function

Generate a Thomae's function (also known as popcorn or raindrop function).

Draw Dirichlet's Function

Generate a Dirichlet's function.

Convert Words to Numbers

Convert numbers as English text to actual digits.

Convert Numbers to Words

Convert numbers to written English text.

Convert Decimal Notation to Scientific Notation

Convert numbers written in decimal form to scientific form.

Convert Scientific Notation to Decimal Notation

Convert numbers written in scientific form to decimal form.

Round Numbers Up

Apply ceil operation to numbers.

Round Numbers Down

Apply floor operation to numbers.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!