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SVC Fractal Set Generator

World's Simplest Math Tool

Free online Smith-Volterra-Cantor (SVC) set fractal generator. Just press a button and you'll get a Smith-Cantor fractal. There are no ads, popups or nonsense, just an awesome Volterra-Cantor set generator. Press a button – get an SVC fractal. Created by math nerds from team Browserling.

᠎᠎᠎          Tool Options

SVC Size and Iterations

SVC fractal width.
SVC fractal height.
Number of iterative subdivisions
of the starting unit line.

Smith-Volterra Set Colors

SVC set background color.
SVC set fill color.
SVC set segment line
border color.

Other Options for SVC Fractal

SVC set segment line border width.
Padding around the SVC fractal.
Direction of drawing.
Connect the shredded segments
with each other. (Leave no space
between iterations.)
Draw only the last iteration of
the SVC fractal set.

What Is an SVC Fractal Set Generator?

This tool draws the Smith-Volterra-Cantor (SVC) set. The SVC fractal also is known as fat Cantor set and epsilon-Cantor (ε-Cantor). SVC set is very similar to the regular Cantor set but has one key difference. With every new iteration, an ever smaller piece from the unit segment is cut out. In the second iteration we cut the middle 1/4 part, in the third 1/16, in the fourth 1/64, and so on. You can change the length and height of the beginning segment by setting the set dimensions in the options above. Other options include ability to select three colors for drawing the Smith-Volterra-Cantor fractal. These three colors are the background color, the line segment color, and line border color. If you set the line border to 0 px width, then the SVC fractal will be two-colored. You can add padding to line segments and change the line segment length by changing the dimensions of the image. If you enable the squeeze mode then all segments will get stretched vertically and joined together, leaving no space between them. If you enable barcode mode then only the last iteration is drawn and is also stretched vertically creating a barcode-like fractal. You can also select the direction in which the segments will get iterated to. Mathabulous!


SVC Fractal Set Generator Examples

Click to try!

Draw a Smith-Volterra-Cantor Set With a Boundary Line

This example generates SVC fractal with each line segment having an extra 6px white boundary line around it. To do this we use three colors – blue for background, white for border, and black for fill.

Required options
These options will be used automatically if you select this example.
SVC fractal width.
SVC fractal height.
Number of iterative subdivisions
of the starting unit line.
SVC set background color.
SVC set fill color.
SVC set segment line
border color.
SVC set segment line border width.
Padding around the SVC fractal.
Direction of drawing.
Connect the shredded segments
with each other. (Leave no space
between iterations.)
Draw only the last iteration of
the SVC fractal set.

Generate a Squeezed Fat Cantor Set

This example enables the squeeze-mode function. This squeezes all fat Cantor fractal lines together. We also adjust padding to 10px and make the fractal set be square-shaped with size 600x600px.

Required options
These options will be used automatically if you select this example.
SVC fractal width.
SVC fractal height.
Number of iterative subdivisions
of the starting unit line.
SVC set background color.
SVC set fill color.
SVC set segment line
border color.
SVC set segment line border width.
Padding around the SVC fractal.
Direction of drawing.
Connect the shredded segments
with each other. (Leave no space
between iterations.)
Draw only the last iteration of
the SVC fractal set.

Draw an epsilon-Cantor Set Bottom Up

In this example we change the drawing direction and draw the ε-Cantor set facing up. We set a large width (1000 pixels) and small height (400 pixels) and show 6 generations of the fractal.

Required options
These options will be used automatically if you select this example.
SVC fractal width.
SVC fractal height.
Number of iterative subdivisions
of the starting unit line.
SVC set background color.
SVC set fill color.
SVC set segment line
border color.
SVC set segment line border width.
Padding around the SVC fractal.
Direction of drawing.
Connect the shredded segments
with each other. (Leave no space
between iterations.)
Draw only the last iteration of
the SVC fractal set.

Draw an SVC Fractal as a Barcode

This example draws a black and white bar code from the last iteration of SVC fractal. This is achieved by enabling barcode mode in the options. There is no padding here, and seventh subdivision of the set is generated.

Required options
These options will be used automatically if you select this example.
SVC fractal width.
SVC fractal height.
Number of iterative subdivisions
of the starting unit line.
SVC set background color.
SVC set fill color.
SVC set segment line
border color.
SVC set segment line border width.
Padding around the SVC fractal.
Direction of drawing.
Connect the shredded segments
with each other. (Leave no space
between iterations.)
Draw only the last iteration of
the SVC fractal set.

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://onlinetools.com/math/generate-smith-volterra-cantor-set?width=600&height=320&iterations=4&background-color=%25230d02ad&fill-color=black&line-segment-color=white&line-width=6&padding=10&direction=down&squeeze-mode=false&barcode-mode=false

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