Free online Fibonacci word fractal generator. Just press a button and you'll get a Fibonacci word curve. There are no ads, popups or nonsense, just an awesome Fibonacci word fractal generator. Press a button – get a Fibonacci word fractal. Created by math nerds from team Browserling.

Free online Fibonacci word fractal generator. Just press a button and you'll get a Fibonacci word curve. There are no ads, popups or nonsense, just an awesome Fibonacci word fractal generator. Press a button – get a Fibonacci word fractal. Created by math nerds from team Browserling.

This tool draws Fibonacci word fractals. The Fibonacci word fractal is a self-similar plane curve that's generated from Fibonacci words. The rules for drawing the Fibonacci word curve are very simple – if the current Fibonacci word digit is 1, draw a segment, otherwise rotate 90 degrees. Fibonacci words themselves are constructed by concatenating previous two words. The first two words are 0 and 1. As a result, the Fibonacci word curve at every step of iteration is self-similar to previous two iterations. With each step, the curve gets twice as long so we added a bunch of options so you can visualize it better. You have an option to set arbitrary width and height of the fractal, change the thickness and color of the curve, and add padding around the fractal borders. You can also change the background color and set the starting direction of the fractal. Additionally, you can drop the last curve segment to make the fractal more symmetrical. Mathabulous!

This tool draws Fibonacci word fractals. The Fibonacci word fractal is a self-similar plane curve that's generated from Fibonacci words. The rules for drawing the Fibonacci word curve are very simple – if the current Fibonacci word digit is 1, draw a segment, otherwise rotate 90 degrees. Fibonacci words themselves are constructed by concatenating previous two words. The first two words are 0 and 1. As a result, the Fibonacci word curve at every step of iteration is self-similar to previous two iterations. With each step, the curve gets twice as long so we added a bunch of options so you can visualize it better. You have an option to set arbitrary width and height of the fractal, change the thickness and color of the curve, and add padding around the fractal borders. You can also change the background color and set the starting direction of the fractal. Additionally, you can drop the last curve segment to make the fractal more symmetrical. Mathabulous!

Click to try!

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### Draw 16 Iterations of a Fibonacci Word Fractal

**Required options**

This example generates a white Fibonacci word curve on a dark red 400x400 background. It sets the curve starting direction to north (up), changes curve width to 3px and adds 15px of padding around the fractal.

Fibonacci Width

Fibonacci Height

How many iterative steps to make?

Color for background.

Color for Fibonacci word curve.

Thickness of Fibonacci word line.

Extra padding Fibonacci word fractal.

Starting direction of the fractal.

If you skip the last symbol, the
Fibonacci word fractal becomes
more symmetrical.

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### Generate a Stretched Fibonacci Word Curve

**Required options**

In this example we draw a horizontally-stretched Fibonacci word fractal. The width is set to 800px and height is set to 500px. It uses 15 iterations here and removes the last curve segment for a more symmetric look.

Fibonacci Width

Fibonacci Height

How many iterative steps to make?

Color for background.

Color for Fibonacci word curve.

Thickness of Fibonacci word line.

Extra padding Fibonacci word fractal.

Starting direction of the fractal.

If you skip the last symbol, the
Fibonacci word fractal becomes
more symmetrical.

click me
### Draw a Symmetrical Fibonacci Word Fractal

**Required options**

This example generates a Fibonacci word curve using 20 iterations. The starting direction is set to east (left) and it uses green and black colors for the fractal drawing. This fractal shows mirror symmetry along the middle.

Fibonacci Width

Fibonacci Height

How many iterative steps to make?

Color for background.

Color for Fibonacci word curve.

Thickness of Fibonacci word line.

Extra padding Fibonacci word fractal.

Starting direction of the fractal.

If you skip the last symbol, the
Fibonacci word fractal becomes
more symmetrical.

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-fibonacci-word-fractal?width=400&height=400&iterations=16&background-color=%252366003f&line-segment-color=white&line-width=3&padding=15&direction=up&skip-last-symbol=false

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Quickly generate a list of Fibonacci primes.

Quickly generate a list of Fibonacci words.

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Quickly generate a list of Lucas numbers.

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Quickly generate random numbers.

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Quickly generate a list of even numbers.

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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.

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Quickly create a matrix with random elements.

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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.

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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.

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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.

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We're Browserling — a friendly and fun cross-browser testing company powered by alien technology. At Browserling we love to make people's lives easier, so we created this collection of math tools. Unlike many other math tools that require advanced math knowledge, we made our tools as simple as possible. All tools have the same user interface and they are enjoyed by millions of users every month. Our math tools are actually powered by our web developer tools that we created over the last couple of years. Check them out!

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