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I'm a little new using QGIS.

I know how to add random points within a geometry but how can I add multiple correctly distributed points within a polygon?

Like this

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Not Like this

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    Are you trying to symbolize the existing polygons with dots, or are you trying to create a new point data layer(s) that fall within the polygon boundary? – Stu Smith Sep 30 '19 at 23:12
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You can use the tool called "regular points" (Vector-> Research Tools) in QGIS to make the points layer.

Use your polygon layer as the extent, and adjust the point spacing to get the point density how you want it. Here's what the window looks like: Regular Points Window

You'll want to use either the clip or intersect tool to get only the points that fall into your polygon.

https://docs.qgis.org/testing/en/docs/user_manual/processing_algs/qgis/vectorcreation.html

Look at @Aaron's answer here: Generating regular sample points in a polygon

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