How to generate random points in a circular distribution

Question

I am wondering how i could generate random numbers that appear in a circular distribution.

I am able to generate random points in a rectangular distribution such that

Answer 1

What you need is to sample from (polar form):

r, theta = [math.sqrt(random.randint(0,500))*math.sqrt(500), 2*math.pi*random.random()]

You can then transform r and theta back to cartesian coordinates x and y via

x = 500 + r * math.cos(theta) 
y = 500 + r * math.sin(theta)

Related (although not Python), but gives the idea.