How to generate a normal distribution with variance $\sigma^2= 0.08$
To generate normal random variable, you can use numpy.random.normal where the scale parameter is the standard deviation. To generate multivariate normal random variable, you can use numpy.random.multivariate_normal.

If you are an R user, you might like to consider mvrnorm

However, I doubt that is what you really want. After all, it is possible to generate points that are beyond the square. 

You might like to consider some bounded distribution instead. Consider truncated normal distribution or uniform distribution.