(Example of variegated yarn)

The difference between self-striping and variegated yarn is the length of the color repeats in the yarn. With self-striping yarn those repeats are exactly measured and each color is the same length and they result in stripes, while in variegated yarn can vary from very short color repeats to very long color repeats.

Same patterns will look completely different if you make them with these types of yarn. 

People turn to variegated yarn because there is no extra effort in deciding on the color-palette, and the changing/ additions of new colors in the rows/rounds. Projects with this yarn are
Self-striping yarn creates stripes and is most suitable for blankets, scarves and sweaters.  
I love both but tend to tilt towards self-striping more. You?
 

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