# Koch triangle fractal generator

## World's simplest math tool

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

announcement
heads up!

We just launched a new site — Online TEXT Tools — utilities for text processing. Check it out!

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

Can't convert.

Koch triangle fractal generator tool
What is a koch triangle fractal generator?

This tool draws Koch triangle fractals. Here's how it works. The fractal starts from the basis figure, which is an equilateral triangle. The triangle is then decomposed into three separate lines – its sides. Now each line gets deformed into a three-segment zigzag where the angle between zigs and zags is 108 degrees. This process is then repeated for all new zigzags as many times as you specify in the iterations field. With this tool you can generate, explore and draw your own creative Koch triangles using a variety of customization options. In particular, you can make fractals very colorful by using three custom colors for zigzags, for entire fractal fill and for background. You can remove the fill by leaving the fill-color input field empty, and you can also remove the zigzag color by making zigzag thickness equal to zero. You can rotate the Koch fractal in 4 different positions and add an indent from all its sides. Finally, you can save the finished fractal in as detailed size you need by specifying the width and height of the image in pixels. Mathabulous!

Koch triangle fractal generator examples
Click to use

Contrasting Colors

This example draws the Koch triangle using bright and contrasting fill and background colors. It uses a 2px black line for zigzags and draws 5th generations of triangles. The canvas is a square at 400x400 pixels with an inside padding of 10 pixels.

**Required options**

Koch triangle width.

Koch triangle height.

How many times to apply
the zigzap operation?

Koch triangle's
background color.

Koch triangle's
zigzag color.

Koch triangle's
fill color.

Zigzag thickness.

Indent in pixels from all
sides of the canvas.

No Border

In this example we left the zigzag width field empty thereby removing it from the fractal and creating a two-colored Koch fractal. We also set the fractal generator to perform 7 zigzag splitting operations, rotated it 90 degrees by changing the direction to up and streteched it to entire 500 by 500 px canvas area by leaving the padding option empty.

**Required options**

Koch triangle width.

Koch triangle height.

How many times to apply
the zigzap operation?

Koch triangle's
background color.

Koch triangle's
zigzag color.

Koch triangle's
fill color.

Zigzag thickness.

Indent in pixels from all
sides of the canvas.

Koch Triangle Island

This example generates a Koch triangle using 11 iterations. Because it's generating so many iterations the fractal starts to look like an island. The shape of this island is also modified to rectangular 600px-by-500px.

**Required options**

Koch triangle width.

Koch triangle height.

How many times to apply
the zigzap operation?

Koch triangle's
background color.

Koch triangle's
zigzag color.

Koch triangle's
fill color.

Zigzag thickness.

Indent in pixels from all
sides of the canvas.

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-triangle-fractal?&width=400&height=400&iterations=5&background-color=%2340d400&line-segment-color=black&fill-color=%23ff4a3a&line-width=5&padding=10&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 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!