Our Network


Coming Soon


Coming Later

paperfolding sequence generator

world's simplest math tool

Free online regular paperfolding sequence (also known as dragon curve) generator. Just specify how many dragon curve numbers you need and you'll automatically get that many sequence elements. There are no ads, popups or nonsense, just an awesome dragon curve calculator. Press button, get paperfolding sequence. Created by math nerds from team Browserling.

᠎᠎᠎          Tool Options

Paperfolding Generator Options

Start generating paperfolding
numbers from this element.
How many paperfolding
numbers to generate?
Paperfolding element separator.
(Newline \n by default.)

What is a paperfolding sequence generator?

This tool calculates regular paperfolding sequence numbers. This sequence is also known as dragon curve sequence and you can use it to generate the dragon fractal. Dragon curve sequence starts with 1 and each next term is a previous term with 1 and 0 inserted before and after each digit. You can customize how many sequence numbers you need, which sequence element to start with, and which character to use for separating sequence elements. Mathabulous!


Paperfolding sequence generator examples

Click to try

Generate Six Paperfolding Numbers

This example calculates first 6 dragon curve numbers starting from 1st.

1 110 1101100 110110011100100 1101100111001001110110001100100 110110011100100111011000110010011101100111001000110110001100100
Required options
These options will be used automatically if you select this example.
Start generating paperfolding
numbers from this element.
How many paperfolding
numbers to generate?

Calculate Five Dragon Curve Numbers

This example generates 5 paperfolding elements starting from the 3rd and changes separator between numbers to a pipe symbol.

1101100 | 110110011100100 | 1101100111001001110110001100100 | 110110011100100111011000110010011101100111001000110110001100100 | 1101100111001001110110001100100111011001110010001101100011001001110110011100100111011000110010001101100111001000110110001100100
Required options
These options will be used automatically if you select this example.
Start generating paperfolding
numbers from this element.
How many paperfolding
numbers to generate?
Paperfolding element separator.
(Newline \n by default.)

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://onlinetools.com/math/generate-paperfolding-sequence?start=1&count=6

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!
L-system Generator

Quickly visualize rules of an Lindenmayer rewrite system.

Generate Prime Numbers

Quickly generate a list of primes.

Generate Fibonacci Numbers

Quickly generate a list of Fibonacci numbers.

Generate Negafibonacci Numbers

Quickly generate a list of extended, negative Fibonacci numbers.

Generate Fibonacci Primes

Quickly generate a list of Fibonacci primes.

Generate Fibonacci Words

Quickly generate a list of Fibonacci words.

Generate Tribonacci Words

Quickly generate a list of Tribonacci words.

Generate Lucas Numbers

Quickly generate a list of Lucas numbers.

Generate Negalucas Numbers

Quickly generate a list of extended, negative Lucas numbers.

Generate Lucas Primes

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

Generate Abundant Number Sequence

Quickly create a list of excessive numbers.

Generate Deficient Number Sequence

Quickly create a list of deficient numbers.

Generate Perfect Numbers

Quickly generate a list of perfect numbers.

Generate Almost Perfect Numbers

Quickly create a list of slightly defective numbers.

Generate Random Numbers

Quickly generate random numbers.

Generate Look-and-say Sequence

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

Generate Prouhet-Thue-Morse Sequence

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

Generate Paperfolding Sequence

Quickly create a list of dragon curve sequence values.

Generate Kolakoski Sequence

Quickly create a list of Oldenburger-Kolakoski sequence values.

Generate Gijswijt's Sequence

Quickly create a list of Gijswijt sequence values.

Generate Rudin-Shapiro Sequence

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

Generate Baum-Sweet Sequence

Quickly create a list of Baum-Sweet sequence values.

Generate Moser-de Bruijn Sequence

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

Generate Even Numbers

Quickly generate a list of even numbers.

Generate Odd Numbers

Quickly generate a list of odd numbers.

Find All Divisors of a Number

Quickly find all factors of the given integer.

Find Prime Factors

Quickly decompose integers into their prime factors.

Test if a Number is a Prime

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

Test if a Number is Fibonacci

Quickly check if the given number is a Fibonacci number

Generate Pi Digits

Quickly generate π constant's digits to arbitrary precision.

Generate e Digits

Quickly calculate Euler constant's digits to arbitrary precision.

Generate Golden Ratio Digits

Quickly calculate φ constant's digits to arbitrary precision.

Calculate a Factorial

Quickly calculate factorials.

Generate Pascal's Triangle

Quickly create a triangluar array of binomial coefficients.

Generate Random Matrices

Quickly create a matrix with random elements.

Generate an Identity Matrix

Quickly create a unit matrix with ones along the diagonal.

Transpose a Matrix

Quickly find the transpose of a matrix.

Invert a Matrix

Quickly find the inverse of a matrix.

Find the Determinant of a Matrix

Quickly calculate the determinant of a matrix.

Add Matrices

Quickly find the sum of two or more matrices.

Subtract Matrices

Find the difference of two or more matrices.

Multiply Matrices

Quickly find the product of matrices.

Generate a Hilbert Curve

Quickly draw a Hilbert space-filling curve.

Generate a Heighway Triangle

Quickly draw a Heighway triangle fractal.

Generate a Dragon Curve

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

Generate a Twindragon Curve

Quickly draw a Davis-Knuth dragon fractal.

Generate a Terdragon Curve

Quickly draw a triple dragon fractal.

Generate a Quaddragon Curve

Quickly draw a quaddragon fractal.

Generate a Hexadragon Fractal

Quickly draw a hexdragon curve.

Generate a Peano Curve

Quickly draw a Peano space-filling fractal.

Generate a Moore Curve

Quickly draw a Moore space-filling curve.

Generate a Gosper Curve

Quickly draw a Peano-Gosper space-filling curve.

Generate a Sierpinski Arrowhead Curve

Quickly draw a Sierpinski arrowhead fractal curve.

Generate a Sierpinski Triangle

Quickly draw a Sierpinski sieve fractal.

Generate a Sierpinski Curve

Quickly draw a Sierpinski closed plane fractal curve.

Generate a Sierpinski Carpet

Quickly draw a Sierpinski carpet fractal.

Generate a Sierpinski Maze

Quickly draw a Sierpinski maze fractal.

Generate a Sierpinski Square

Quickly draw a Sierpinski square fractal.

Generate a Sierpinski Pentagon

Quickly draw a Sierpinski pentaflake fractal.

Generate a Sierpinski Hexagon

Quickly draw a Sierpinski hexaflake fractal.

Generate a Sierpinski Polyflake

Quickly draw a Sierpinski n-gon fractal.

Generate a Koch Star

Quickly draw a Koch island fractal curve.

Generate a Koch Anti-snowflake

Quickly draw a Koch antisnowflake fractal.

Generate a Koch Triangle

Quickly draw a Koch triangle fractal.

Generate a Koch Polyflake

Quickly draw a Koch n-gon fractal.

Generate a Quadratic Koch Island

Quickly draw a quadratic Koch flake fractal.

Generate a Cesaro Fractal

Quickly draw a Cesaro fractal.

Generate a Cesaro Polyflake

Quickly draw a Cesaro n-gon fractal.

Generate a Triflake Curve

Quickly draw a triflake fractal.

Generate a Quadratic Cross Fractal

Quickly draw a quadric cross fractal.

Generate a Levy C Curve

Quickly draw a self-similar Levy C fractal curve.

Generate a Vicsek Fractal

Quickly draw a Vicsek snowflake fractal.

Generate a T-square Fractal

Quickly draw a T-square fractal.

Generate a Cantor Set

Quickly draw a Cantor set fractal.

Generate an Asymmetric Cantor Set

Quickly draw an asymmetric Cantor set fractal.

Generate a Generalized Cantor Set

Quickly draw a generalized Cantor set fractal.

Generate a Smith-Volterra-Cantor Set

Quickly draw an ε-Cantor set fractal.

Generate a Cantor Dust Fractal

Quickly draw a Cantor dust fractal.

Generate a Pythagoras Tree Fractal

Quickly draw a Pythagoras tree fractal.

Generate a Fibonacci Word Fractal

Quickly draw a Fibonacci word fractal.

Generate an H-Fractal

Quickly draw an H-tree fractal.

Generate a V-tree Fractal

Quickly draw a V-tree fractal.

Generate a Z-Order Curve

Quickly generate a Morton Z-order fractal curve.


Coming Soon

These math tools are on the way!
Clock-walk Digits

Walk a number digit-by-digit following the clock hour hand.

Plot a Function

Draw graphs of mathematical functions.

Draw a LaTeX Formula

Create an image from a LaTeX expression.

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.

Calculate e Digit Sum

Find the sum of e digits.

Calculate Golden Ratio Digit Sum

Find the sum of Golden Ratio digits.

Calculate Pi Digit Sum

Find the sum of pi digits.

Generate Champernowne Digits

Generate Champernowne constant's digits.

Generate Supergolden Ratio Digits

Generate supergolden ratio constant's digits.

Find n-th Champernowne Digit

Calculate the n-th digit of Champernowne constant.

Decode a Look-and-say Sequence

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

Generate P-adic Expansions

Calculate p-adic expansions of arbitrary numbers.

Generate Pandigital Number Sequence

Create a list of pandigital numbers.

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 Triangular Number Sequence

Create a list of triangle 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 Narayana's Cow Sequence

Create a list of Narayana's cow 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.

Continue a Number Sequence

Find a pattern in a number sequence and extend it.

Partition a Number

Find all partitions of the given integer.

Generate Tribonacci Numbers

Create a list of Tribonacci numbers.

Generate Tetranacci Numbers

Create a list of Tetranacci numbers.

Generate Pentanacci Numbers

Create a list of Pentanacci numbers.

Generate n-nacci Numbers

Create a list of higher order Fibonacci numbers.

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 Polynomial Progression

Create a polynomial 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.

Sort a Matrix

Sort matrix rows or columns.

Clamp a Matrix

Set an allowed range for all matrix values.

Randomize a Matrix

Shuffle all elements of a matrix.

Delete Matrix Rows

Delete one or more rows of the given matrix.

Delete Matrix Columns

Delete one or more columns of the given matrix.

Replace Matrix Elements

Replace certain matrix elements with other values.

Set Matrix Determinant

Create a matrix with the given determinant.

Create a Rotation Matrix

Create a rotation matrix from the given angle.

Decode a Rotation Matrix

Find the angle from the given rotation matrix.

Generate a Custom Matrix

Generate a matrix with specific properties and elements.

Generate a Dense Matrix

Generate a matrix with very few zero elements.

Generate a Sparse Matrix

Generate a matrix with very few non-zero elements.

Generate a Singular Matrix

Generate a degenerate matrix with a zero determinant.

Generate a Zeros Matrix

Generate a matrix with all 0's as elements.

Generate a Ones Matrix

Generate a matrix with all 0's as elements.

Generate a Binary Matrix

Generate a matrix with 0's and 1's as elements.

Generate a Square Matrix

Generate a matrix with n rows and n columns (n×n matrix).

Generate a Symmetric Matrix

Generate a matrix with symmetric elements along the diagonal.

Generate a Triangular Matrix

Generate an upper-triangular or lower-triangular matrix.

Generate a Diagonal Matrix

Generate a matrix with elements placed only on the diagonal.

Generate an Orthogonal Matrix

Generate a matrix with orthogonal rows and columns.

Multiply a Matrix by a Scalar

Multiply all matrix elements by a number.

Multiply a Matrix by a Vector

Multiply a matrix by a column vector.

Multiply a Vector by a Matrix

Multiply a row vector by a matrix.

Split a Matrix into Vectors

Create m or n vectors from an m×n matrix (from rows or cols).

Check if a Matrix is Singular

Determine if a matrix is degenerate.

Find Matrix Dimensions

Find the number of rows and columns of a matrix.

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 the eigenvalues of a matrix.

Find Matrix Trace

Find the sum of main diagonal elements of a matrix.

Find Matrix Diagonal Sum

Find the sum of all diagonals or antidiagonals of a matrix.

Find Matrix Row Sum

Find the sum of each row of a matrix.

Find Matrix Column Sum

Find the sum of each column of a matrix.

Find Matrix Element Sum

Find the sum of all matrix elements.

Find Matrix Element Product

Find the product of all matrix elements.

Prettify a Matrix

Beautify a matrix by neatly aligning all its columns.

Reformat a Matrix

Convert a matrix in one format to another format.

Visualize a Vector

Draw a 2d or 3d vector to show its magnitude and angle.

Sort a Vector

Sort vector components.

Clamp a Vector

Set the allowed range for all vector components.

Randomize a Vector

Randomize the order of vector components.

Truncate a Vector

Delete vector components.

Replace Vector Components

Replace certain vector components with other values.

Prettify a Vector

Beautify a vector and neatly align all its components.

Reformat a Vector

Convert a vector in one format to another format.

Transpose a Vector

Convert a row-vector to column-vector.

Duplicate a Vector

Create multiple copies of the same vector.

Increment a Vector

Increment vector components.

Decrement a Vector

Increment vector components.

Rotate a Vector

Rotate a vector by any angle.

Scale a Vector

Shrink or enlarge a vector by a constant factor.

Calculate Vector Angle

Find the angle that's formed between two vectors.

Set Vector Angle

Create pairs of vectors with a specific angle.

Normalize a Vector

Create a unit vector of length one from any given vector.

Generate a Random Vector

Create one or more random vectors of any length.

Generate a Custom Vector

Create custom vectors with specific components.

Generate a Dense Vector

Create a vector with very few zero components.

Generate a Sparse Vector

Create a vector with many zero components.

Generate a Null Vector

Create a vector all components equal to zero.

Generate a Ones Vector

Create a vector all components equal to one.

Generate a Unit Vector

Create one or more random vectors of length one.

Generate Opposite Vectors

Create pairs of antiparallel vectors.

Generate Parallel Vectors

Create pairs of parallel vectors.

Generate Perpendicular Vectors

Create pairs of perpendicular vectors.

Generate Orthogonal Vectors

Create pairs of orthogonal vectors.

Generate Orthonormal Vectors

Create pairs of perpendicular unit vectors of length one.

Find Vector Norm

Calculate L₁, L₂, L₃, L₄, L₅, and other vector norms.

Find Vector Length

Calculate the length of a vector.

Set Vector Length

Create vectors with a specific length.

Find Vector Dot Product

Calculate the scalar product of two vectors.

Set Vector Dot Product

Find two vectors with a specific scalar product value.

Find Vector Cross Product

Calculate the cross product of two vectors.

Set Vector Cross Product

Find two vectors with a specific cross product value.

Find Scalar Triple Product

Calculate the mixed product of three vectors.

Find Vector Triple Product

Calculate the vector triple product (back of the cab).

Find Scalar Quadruple Product

Calculate the scalar quadruple product of four vectors.

Find Vector Quadruple Product

Calculate the vector product of four vectors.

Mix Vectors

Mix the components of multiple vectors.

Join Vectors

Concatenate two or more vectors.

Add Vectors

Find the sum of two or more vectors.

Multiply Vectors

Multiply two or more vectors.

Multiply Vector by Constant

Multiply all vector components by a scalar value.

Find Vector Component Sum

Find the sum of all vector components.

Find Vector Component Product

Find the product of all vector components.

Find Vector Dimensions

Find the number of components in a vector.

Calculate Sine

Calculate the sine of an angle.

Visualize Sine

Draw the sine function.

Calculate Arcsine

Calculate the arcsine of an angle.

Visualize Arcsine

Draw the arcsine function.

Calculate Cosine

Calculate the cosine of an angle.

Visualize Cosine

Draw the cosine function.

Calculate Arccosine

Calculate the arccosine of an angle.

Visualize Arccosine

Draw the arccosine function.

Calculate Tangent

Calculate the tangent of an angle.

Visualize Tangent

Draw the tangent function.

Calculate Cotangent

Calculate the cotangent of an angle.

Visualize Cotangent

Draw the cotangent function.

Calculate Cosecant

Calculate the cosecant of an angle.

Visualize Cosecant

Draw the cosecant function.

Calculate Secant

Calculate the secant of an angle.

Visualize Secant

Draw the secant function.

Draw All Trigonometric Functions

Visualize all trigonometric functions at once.

Draw an Archimedean Spiral

Generate an Archimedean spiral curve.

Draw an Euler Spiral

Generate a Cornu spiral curve (polynomial spiral).

Draw a Fibonacci Spiral

Generate a Fibonacci spiral curve.

Draw a Theodorus Spiral

Generate a square root spiral.

Draw a Fermat Spiral

Generate a parabolic 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.

Draw a Gabriel's Horn

Draw a geometric figure with infinite surface area and finite volume.

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.

Analyze Numbers

Count how many times each number appears.

Rewrite a Number as a Sum

Create a sum that adds up to the given number.

Rewrite a Number as a Product

Create a product that multiplies up to the given number.

Generate a Multiplication Table

Draw an n×m multiplication table.

Generate an Addition Table

Draw an n×m addition table.

Generate a Division Table

Draw an n×m division table.

Generate a Modular Arithmetic Table

Draw an n×m modular arithmetic table for any modulus.

Draw a Pie Chart

Draw a pie chart and show relative sizes of data.

Draw a Bar Chart

Draw a bar chart and visualize data.

Draw a Column Chart

Draw a column chart and visualize data.

Draw a Line Chart

Draw a line chart and visualize data.

Draw an Area Chart

Draw an area chart and visualize data.

Visualize Percentage

Draw a chart that shows percentage.

Tile a Plane

Fill a plane by convex regular polygons.

Flip a Coin

Toss a coin and get head or tails.

Roll a Dice

Throw a dice and get a number on its side.

Generate a Maze

Draw a maze of any size and complexity.


Subscribe!

Subscribe to our updates. We'll let you know when we release new tools, features, and organize online workshops.

Enter your email here


Feedback. We'd love to hear from you! 👋