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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 mathematicians for mathematicians.
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Fractal Size and Steps
Fibonacci Width
Fibonacci Height
How many iterative steps to make?
Fractal Colors
Color for background.
Color for Fibonacci word curve.
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.
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 concatenting 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've an option to set arbitrary width and height of the fractal, then thickness and color of the curve, and padding around fractal borders. You can also change 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
These options will be used automatically if you select this example.
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.
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
These options will be used automatically if you select this example.
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.
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
These options will be used automatically if you select this example.
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.
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
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