onlinemathtools logo

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.
announcement heads up!
We just launched a new site — Online UTF8 Tools — utilities for working with UTF8 encoding. Check it out!
Size, Order, Base and Bend
Koch polygon's width.
Koch polygon's height.
Koch polygon's iterations.
Number of base polygon's sides.
Bend angle of zigzag segments.
Koch Polygon's Colors
Background color for Koch's polyflake.
Koch polyflake's zigzag color.
Koch polyflake's fill color.
Zigzag, Padding and Direction
Koch polygon's border width.
Padding around Koch's polygon.
Start drawing Koch's n-gon in this direction.
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.
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
These options will be used automatically if you select this example.
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.
Start drawing Koch's n-gon in this direction.
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.
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
These options will be used automatically if you select this example.
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.
Start drawing Koch's n-gon in this direction.
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.
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
These options will be used automatically if you select this example.
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.
Start drawing Koch's n-gon in this direction.
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.
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
These options will be used automatically if you select this example.
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.
Start drawing Koch's n-gon in this direction.
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.
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
These options will be used automatically if you select this example.
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.
Start drawing Koch's n-gon in this direction.
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
Didn't find the tool you were looking for? Let us know what tool we are missing and we'll build it!
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 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.