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This question already has an answer here:

i wanna generate euclodian distance map for my road data. I 'll use it for multi criteria analysis. I can get it by using Arcgis Euclodian Distance tool but i wanna generate it in QGIS environment. I got Sextante plugin and enabled Grass and Saga tools. But i dont know which tool i must use ??? There is a link about ouput of this anaylsis (below image).

ESRI The Euclidean distance example

marked as duplicate by Devdatta Tengshe, MappaGnosis, underdark Mar 1 '13 at 9:10

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Try the Proximity tool. It does the same thing as Euclidean distance. It also gives you the option of specifying a distance in terms of number of cells. I've included some pictures to show you where to find it.

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