how to group clusters?

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Using python and opencv most recent versions.

I have an image like this one:

When the red dots appear, their position always random, so I don't know where they will be next time, this is just as an example. However there are 3 facts:

1. I will have the x, y coordinates of each dot
2. There will always be at least 3 clustered dots and the rest spread out elsewhere.
3. There will always be only one cluster. It is possible that another 2 dots are closed together, but only 3 close dots will be considered clusters.

I want to detect where the cluster is and draw a shape around them. The expected output should be like this:

Since I don't know where they will appear, if I use a red dot as a reference to measure distance, it is possible that one will be outside the cluster. If I try to determine if the dot is in the cluster measuring their x position, it is possible the next cluster will be further away and the spread out dots will be closer on the x side.

I have thought about measuring the distance of each dot against all others and set a threshold of a determined amount of pixels. After that, somehow draw the shape, but I just have no idea of how to do this.

The dots don't really contain any information besides their location (x,y).

Any ideas on how to solve this would be appreciated.