Parents' configuration and numbers of the offspring cluster sizes are generated by the same way as the Thomas model. Let random variable $U_k, k=1,2$ be independently and uniformly distributed in [0,1].
Then $r$ satisfies as follows:
$$r = \sigma_1 \sqrt{-2 \log(1-U_1)}, \; U_2 \le a,$$
$$r = \sigma_2 \sqrt{-2 \log(1-U_1)}, \; otherwise.$$
Then, by the isotropy condition, for $i = 1,2,...,Poisson(mu)$,
coordinate of the offspring points $(x_j^i, y_j^i), j=1,2,...,Poisson(nu)$ is given for each $i=1,...,Poisson(mu)$,
$$x_j^i = x_i^p + r \cos(2 \pi U),$$
$$y_j^i = y_i^p + r \sin(2 \pi U),$$
using series of different uniform random numbers ${U_1, U_2, U}$ for different $i$ and $j$.