# Asymmetric cantor set generator

## World's simplest math tool

Free online asymmetric Cantor set fractal generator. Just press a button and you'll get an asymmetric Cantor fractal. There are no ads, popups or nonsense, just an awesome asymmetric fractal generator. Press a button – get an asymmetric Cantor set. Created by mathematicians for mathematicians.

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Asymmetric cantor set generator tool
What is a asymmetric cantor set generator?

This tool draws asymmetric Cantor set fractals. The asymmetric Cantor set is similar to the regular Cantor set but here the length of the unit line is divided into two uneven parts. You can control the asymmetry of the fractal using two parameters. Alpha determines the length of the segment we draw on the left side. Gamma determines the length of the segment we delete right after drawing the left segment. The length of the remaining right part is determined automatically. In the regular asymmetric fractal both parameters equal to 0.25. With this tool you can explore the behavior of this asymmetric fractal by changing alpha, gamma and various other options. You can increase the depth of the fractal by increasing the number of iterations. You can set the required width and height of the fractal. You can add colors to the fractal. You can set the direction in which lines are divided. You can change padding around the edges of the fractal. You can add a border around subdivided lines and change the thickness of the border. And finally, you can use two additional options that will give the fractal an unusual look. The first one, called squeeze option, will remove all the spacing between the lines, and the second one, called barcode option, will show only the final line splitting. Mathabulous!

Asymmetric cantor set generator examples
Click to use

Generate a Fourth Order Asymmetric Cantor Set Fractal

In this example we draw 4 iterations of the asymmetric Cantor fractal on a 350x350 canvas. We use blue colors for the fractal line and background, and we also draw a 4 pixel wide border around every fractal line segment.

**Required options**

Asymmetric Cantor fractal width.

Asymmetric Cantor fractal height.

How many times should we
divide the initial unit line?

Alpha determines the portion
of the first (left) line segment.

Gamma specifies the portion
of the remaining line segment
to cut.

Background color.

Line segment fill color.

Line segment border color.

Thickness of segment border.
(If it's 0 then no border is drawn.)

Padding around the canvas.

Remove all space between
asymetric fractal generations.

Draw only the last generation of
asymmetric Cantor fractal.

Draw an Asymmetric Cantor Set Without Spacing

This example generates a 5th order fractal and sets the squeeze mode on. When this mode is on, the space between the line segments is removed. All divided line intervals are merged together vertically.

**Required options**

Asymmetric Cantor fractal width.

Asymmetric Cantor fractal height.

How many times should we
divide the initial unit line?

Alpha determines the portion
of the first (left) line segment.

Gamma specifies the portion
of the remaining line segment
to cut.

Background color.

Line segment fill color.

Line segment border color.

Thickness of segment border.
(If it's 0 then no border is drawn.)

Padding around the canvas.

Remove all space between
asymetric fractal generations.

Draw only the last generation of
asymmetric Cantor fractal.

Generate an Asymmetric Cantor Set from Right to Left

In this example we draw the fractal from right to left. The unit line segment is drawn on the right side and it's cut and iterated to the left side. We also set non-square height and width, so we get a rectangular fractal, measuring 600x300 pixels.

**Required options**

Asymmetric Cantor fractal width.

Asymmetric Cantor fractal height.

How many times should we
divide the initial unit line?

Alpha determines the portion
of the first (left) line segment.

Gamma specifies the portion
of the remaining line segment
to cut.

Background color.

Line segment fill color.

Line segment border color.

Thickness of segment border.
(If it's 0 then no border is drawn.)

Padding around the canvas.

Remove all space between
asymetric fractal generations.

Draw only the last generation of
asymmetric Cantor fractal.

Draw an Asymmetric Cantor Set in the Form of Stairs

This example uses alpha and gamma arguments to draws a fractal with a very large first segment (alpha = 0.8), with a small cut (gamma = 0.19), and an infinitesimal second segment (0.01). Further by enabling the squeeze mode and changing fractal's orientation to right all the lines are joined and it makes the asymmetric Cantor set look like a staircase.

**Required options**

Asymmetric Cantor fractal width.

Asymmetric Cantor fractal height.

How many times should we
divide the initial unit line?

Alpha determines the portion
of the first (left) line segment.

Gamma specifies the portion
of the remaining line segment
to cut.

Background color.

Line segment fill color.

Line segment border color.

Thickness of segment border.
(If it's 0 then no border is drawn.)

Padding around the canvas.

Remove all space between
asymetric fractal generations.

Draw only the last generation of
asymmetric Cantor fractal.

Generate a Symmetric Cantor Set Fractal

In this example, the alpha parameter is 0.4 and the gamma is 0.2. The second part of the segment is determined automatically and it's also equal to 0.4 (1 - alpha - gamma = 1 - 0.4 - 0.2). Consequently, we draw two equal segments on both sides and the fractal becomes symmetric.

**Required options**

Asymmetric Cantor fractal width.

Asymmetric Cantor fractal height.

How many times should we
divide the initial unit line?

Alpha determines the portion
of the first (left) line segment.

Gamma specifies the portion
of the remaining line segment
to cut.

Background color.

Line segment fill color.

Line segment border color.

Thickness of segment border.
(If it's 0 then no border is drawn.)

Padding around the canvas.

Remove all space between
asymetric fractal generations.

Draw only the last generation of
asymmetric Cantor fractal.

Draw an Asymmetric Cantor Barcode

This example generates just the final generation of the fractal. This is done by enabling the interesting barcode option. It uses a bright green for vertical lines and a dark blue background color.

**Required options**

Asymmetric Cantor fractal width.

Asymmetric Cantor fractal height.

How many times should we
divide the initial unit line?

Alpha determines the portion
of the first (left) line segment.

Gamma specifies the portion
of the remaining line segment
to cut.

Background color.

Line segment fill color.

Line segment border color.

Thickness of segment border.
(If it's 0 then no border is drawn.)

Padding around the canvas.

Remove all space between
asymetric fractal generations.

Draw only the last generation of
asymmetric Cantor fractal.

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-asymmetric-cantor-set?&width=350&height=350&iterations=4&background-color=%230359d9&fill-color=%23050d54&line-segment-color=white&line-width=4&padding=8&direction=down&squeeze-mode=false&barcode-mode=false&alpha=0.25&gamma=0.25

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