What cubic function can I use to get a random distribution biased towards the middle-CodePudding

I want a circle with more circles inside it (doesn't strictly need to be inside it). The position of inner circles are determined randomly in a way that there should be most circles at the centre and less and less and it goes out towards the edge of the circle.

From

I know that the rest of the code is correct because I used another function mentioned in that answer (f(X)=2X/(1 X)) and it gives the right distribution, biased towards the higher values:

def distBiasedUpper(_min, _max):
    r = lambda : random.uniform(0, 1)
    r1, r2 = r(), r()
    bias = lambda _r: (2 * _r / (1   _r)) * (1   _max - _min)   _min
    return (bias(r1), bias(r2))

CodePudding user response：

Actually you are generating random numbers in the range [0.0, 1.0] and assigning them to the range [_min, _max]. Therfore 0 is mapped to _min. As a result, there are more points near _min.
You have to generate random numbers in range [-1.0, 1.0] and map them to the range [_min, _max]. So 0 is in the middle of the range and most of the points are near (_min _max) / 2:

def distBiasedMiddle(_min, _max):
    r = lambda : random.uniform(-1, 1)
    r1, r2 = r(), r()
    bias = lambda _r:  _r**3 * (_max - _min) / 2   (_min   _max) / 2
    return (bias(r1), bias(r2))