onlinemathtools logo

Heighway triangle generator

World's simplest math tool

Free online Heighway triangle fractal generator. Just press a button and you'll get a Heighway triangle. There are no ads, popups or nonsense, just an awesome a Heighway triangle generator. Press a button – get a fractal. 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!
Iterations and Size
Heighway triangle width.
Heighway triangle height.
Number of Heighway triangle iterations.
Heighway Triangles' Colors
Drawing canvas fill color.
Triangles' edge color.
Triangles' fill color.
Thickness, Padding, Direction
Thickness of triangle edges.
Padding around all triangles.
Which way to start drawing triangles?
Heighway triangle generator tool What is a heighway triangle generator?
This tool draws Heighway triangles. You can create your own original Heighway triangle images of arbitrary recursive depth using a three color palette. You can experiment with the number of iterations of the fractal, choose the height and width for the output image, increase or completely remove the thickness of triangles' sides, and make triangles more or less centered by adding or removing pixels from the top, bottom, left and right sides. And one more extra feature is rotation of the triangles. Mathabulous!
Heighway triangle generator examples Click to use
Filling Triangles
This example draws yellow-filled triangles on a bluish dark background. We left the triangle side thickness option unused so the triangles sides aren't drawn in any color and only two colors are used that fill an area of 700 by 700 pixels.
Required options
These options will be used automatically if you select this example.
Heighway triangle width.
Heighway triangle height.
Number of Heighway triangle iterations.
Drawing canvas fill color.
Triangles' edge color.
Triangles' fill color.
Thickness of triangle edges.
Padding around all triangles.
Which way to start drawing triangles?
Tricolored Heighway Triangle
In this example we use all three possible colors for drawing the triangles. The colors here are written in various formats – hex code for the background, named color for the line, and RGB code for the filling. We generate five iterations of the fractal, set the triangles' side width to three pixels and turn all triangles up.
Required options
These options will be used automatically if you select this example.
Heighway triangle width.
Heighway triangle height.
Number of Heighway triangle iterations.
Drawing canvas fill color.
Triangles' edge color.
Triangles' fill color.
Thickness of triangle edges.
Padding around all triangles.
Which way to start drawing triangles?
Heighway Island
In this example we left the fill field empty and generated a fractal by drawing only triangle edges using lines of one pixel width. Despite this the fractal is completely filled with blue color. How is that possible? It's because because we generated 12 iterations of this fractal and all edges of all triangles got so close together that no space was left empty. This fractal is also known as Heighway Island.
Required options
These options will be used automatically if you select this example.
Heighway triangle width.
Heighway triangle height.
Number of Heighway triangle iterations.
Drawing canvas fill color.
Triangles' edge color.
Triangles' fill color.
Thickness of triangle edges.
Padding around all triangles.
Which way to start drawing triangles?
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-heighway-triangle?&width=700&height=700&iterations=6&background-color=%23011f40&line-segment-color=white&fill-color=%23ffff74&line-width=&padding=10&direction=right
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 generate a list of perfect 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 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 quadratic Koch flake fractal.
Quickly draw a Cesaro 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 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.
Test if a Number is a Prime
Find out if the given number is a prime number.
Test if a Number is a Fibonacci Number
Find out if the given number is a Fibonacci number.
Decode a Look-and-say Sequence
Perform the inverse operation on a look-and-say sequence.
Generate Deficient Number Sequence
Create a list of deficient 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 Deficient Number Sequence
Create a list of deficient numbers.
Generate Secant Number Sequence
Create a list of secant numbers.
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 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.