I have generated plots for 250 random realisations of the positions of the Rabbits in the question:
Flopsy, a rabbit, lives in a circular field of radius 25m. We can express Flopsy’s position in terms of $x$ and $y$ co-ordinates $(x_F , y_F )$, where $(0, 0)$ is the centre of the field, the $x$ axis runs from west to east, the $y$ axis runs from south to north, and the units of measurement are metres.
Alternatively, in polar co-ordinates Flopsy’s location is $(\theta_F , r_F )$, where $\theta_F$ is the angle between the x-axis and the line from Flopsy to the origin and $r_F$ is the distance, in m, between Flopsy and the origin.
A second rabbit, Mopsy, lives in the same field. We denote her location by $(x_M, y_M)$ or, in polar co-ordinates, $(\theta_M, r_M)$.
If we observe Flopsy on repeated occasions, her locations can be regarded as independent realisations of a random process in which $\theta_F ∼ \text {Unif}(0, 2\pi)$ and $r_F ∼ \text{Unif}(0, 25)$, and Mopsy's position is $x_M ∼ \text{Unif}(−25, 25)$ and $y_M ∼ \text{Unif}(−25, 25)$.
I get a cluster in the centre of the circle for Flopsy's positions but Mopsy's positions are uniformly distributed across the circle. I can see why Mopsy's positions are uniform around the circle but I would've expected the same for Flopsy as the polar coordinates still follow a uniform distribution, so I cannot see why the cluster is formed.
If you were to plot Flopsy's position on rectangular axes they would be uniformly distributed, but when you move to polar coordinates, it's as if you are wrapping the $\theta$ axis around the pole. Points closer to the original $\theta$ axis will be squeezed together and points far from the original $\theta$ axis will be more spread out.