The unit circle is still present, but it now seems to be getting a few uniform outliers, a sort of halo.
I think that the explanations given in the responses are not correct. Even for the unit circle, they account for why you don't seem many points outside of the interval, but fail to explain why you rarely see points inside of the unit circle. The argument essentially is that inside the unit circle the equation reduces to
a1*x+a0 = 0
But the distribution for this (randomly picking a1 and a0 when you generate the poly) indicates you'd expect the occasional circle that had a point that was about .3 away from the radius. If you generated the circle 10 times, you don't. You rarely get as far as 0.1 .
The unit circle is still present, but it now seems to be getting a few uniform outliers, a sort of halo.
I think that the explanations given in the responses are not correct. Even for the unit circle, they account for why you don't seem many points outside of the interval, but fail to explain why you rarely see points inside of the unit circle. The argument essentially is that inside the unit circle the equation reduces to
But the distribution for this (randomly picking a1 and a0 when you generate the poly) indicates you'd expect the occasional circle that had a point that was about .3 away from the radius. If you generated the circle 10 times, you don't. You rarely get as far as 0.1 .