Consider the two type of the Thomas model with parameters $(mu_1, nu, sigma_1)$ and $(mu_2, nu, sigma_2)$.
Parents' configuration and numbers of the offspring cluster sizes are generated by the two types of uniformly
distributed parents $(x_i^k, x_i^k)$ with $i=1,2,...,Poisson(mu_k)$ for $ k=1,2$, respectively. Then, using series of different uniform random numbers ${U}$ for different $i$ and $j$,
the offspring coordinates $(x_j^{k,i}, y_j^{k,i})$ of the parents $(k,i)$
with $k=1,2$ and $j=1,2,...,Poisson(nu)$ is given by
$$x_j^{k,i} = x_i^k + r_k \cos (2 \pi U),$$
$$y_j^{k,i} = y_i^k + r_k \sin (2 \pi U),$$
where
$$r_k = \sigma_k \sqrt{-2 \log (1-U_k)}, \; k=1,2,$$
with different random numbers ${U_k, U}$ for different $k, i$, and $j$