 # Generalized cantor set generator

## World's simplest math tool

Free online generalized Cantor set fractal generator. Just press a button and you'll get a generalized Cantor fractal. There are no ads, popups or nonsense, just an awesome generalized Cantor set generator. Press a button – get a generalized Cantor set. Created by mathematicians for mathematicians.
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Dimensions, Iterations, Gamma
Generalized set width.
Generalized set height.
Number of set cuts. (Iterations.)
Gamma - defines part of the unit interval to cut from middle. (Must be between 0 and 1).
Background, Foreground, Border
Generalized Cantor set background color.
Generalized Cantor set fill color.
Generalized Cantor set border color.
Padding, Direction, Squeezing
Set segment border width.
Padding around the entire set.
Set growth direction.
Remove all space between line segments.
Draw only the last iterative step.
Generalized cantor set generator tool What is a generalized cantor set generator?
This tool draws generalized Cantor set fractals. The generalized Cantor set is similar to the regular Cantor set but here you can set a special parameter called gamma that determines which part of the initial unit segment gets cut at every iteration. Parameter gamma can vary from 0 to 1. Zero means nothing gets cut, and one means everything gets cut. With this tool you can define gamma as well as change other fractal settings. You can set custom colors for the Cantor fractal and customize background, line, and fill colors. You can also change line width around segments and adjust padding around outer line of segments. This tool also lets you change direction in which fractal cuts are made – you set fractal to go east (left), south (down), west (right) or north (up). Finally there are also two special drawing options – squeeze option that combines all fractal segments together and barcode option that makes the generalized Cantor set fractal look similar to a barcode on product packaging. Mathabulous!
Generalized cantor set generator examples Click to use
Draw a Regular Cantor Fractal
This example sets gamma to 1/3 (or 0.33). This means 1/3 of every line segments gets removed at every iteration. As a result, we get the standard Cantor set, which by definition removes 1/3 from the middle of every line segment. Required options
These options will be used automatically if you select this example.
Generalized set width.
Generalized set height.
Number of set cuts. (Iterations.)
Gamma - defines part of the unit interval to cut from middle. (Must be between 0 and 1).
Generalized Cantor set background color.
Generalized Cantor set fill color.
Generalized Cantor set border color.
Set segment border width.
Padding around the entire set.
Set growth direction.
Remove all space between line segments.
Draw only the last iterative step.
Generate an 8th Order Generalized Cantor Set
This example configures gamma parameter to be 0.1, which cuts one-tenth of every line segment on every iteration. There are 8 recursive iterations and the canvas size is 400x400 pixels. Required options
These options will be used automatically if you select this example.
Generalized set width.
Generalized set height.
Number of set cuts. (Iterations.)
Gamma - defines part of the unit interval to cut from middle. (Must be between 0 and 1).
Generalized Cantor set background color.
Generalized Cantor set fill color.
Generalized Cantor set border color.
Set segment border width.
Padding around the entire set.
Set growth direction.
Remove all space between line segments.
Draw only the last iterative step.
Draw an Upside-down Generalized Cantor Set
In this example we combine all segments vertically and generate our fractal upside down. We get true artwork – a view of a city with high scrapers. Required options
These options will be used automatically if you select this example.
Generalized set width.
Generalized set height.
Number of set cuts. (Iterations.)
Gamma - defines part of the unit interval to cut from middle. (Must be between 0 and 1).
Generalized Cantor set background color.
Generalized Cantor set fill color.
Generalized Cantor set border color.
Set segment border width.
Padding around the entire set.
Set growth direction.
Remove all space between line segments.
Draw only the last iterative step.
Apply Barcode Mode to Generalized Cantor Set
This example sets barcode option to true that makes it skip the first seven iterations and draw only the eighth iteration. This option stretches the final set to the entire image with dimensions 800x500 pixels. Required options
These options will be used automatically if you select this example.
Generalized set width.
Generalized set height.
Number of set cuts. (Iterations.)
Gamma - defines part of the unit interval to cut from middle. (Must be between 0 and 1).
Generalized Cantor set background color.
Generalized Cantor set fill color.
Generalized Cantor set border color.
Set segment border width.
Padding around the entire set.
Set growth direction.
Remove all space between line segments.
Draw only the last iterative step.
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-generalized-cantor-set?&width=450&height=350&iterations=4&gamma=0.33&background-color=%23a6005b&fill-color=white&line-segment-color=black&line-width=10&padding=20&direction=down&squeeze-mode=false&barcode-mode=false
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