# Fibonacci word fractal generator

## World's simplest math tool

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.

announcement
a new project!

Super exciting news! We just launched MATHURLS – a fun math news reader. Check it out!

*fullscreen*

*fullscreen_exit*

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

Can't convert.

Fibonacci word fractal generator tool
What is a fibonacci word fractal generator?

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!

Fibonacci word fractal generator examples
Click to use

Draw 16 Iterations of a Fibonacci Word Fractal

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.

**Required options**

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.

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

Generate a Stretched Fibonacci Word Curve

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.

**Required options**

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.

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

Draw a Symmetrical Fibonacci Word Fractal

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.

**Required options**

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.

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

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-fibonacci-word-fractal?&width=400&height=400&iterations=16&background-color=%2366003f&line-segment-color=white&line-width=3&padding=15&direction=up&skip-last-symbol=false

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.

Calculate Pi Digit Sum

Find the sum of pi digits.

Calculate e Digit Sum

Find the sum of e digits.

Calculate Golden Ratio Digit Sum

Find the sum of Golden Ratio digits.

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 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 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 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.

Generate a Sparse Matrix

Generate a matrix with very few non-zero elements.

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.

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.

Generate a Multiplication Table

Draw an n×m multiplication table.

Flip a Coin

Toss a coin and get head or tails.

Roll a Dice

Throw a dice and get a number on its side.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!