Cluster growth model for treelike structures

We present a cluster growth model for trees (random aggregates without loops). The intrinsic dimension $d_l$ and fractal dimension $d_f$ are adjustable. We study the ‘‘skeletons’’ of trees embedded in d=2, and find that the intrinsic dimension of a skeleton is $d_l^s$=1 for $d_l$≤$d_l^c$≊1.65, and $d_l^s$≊1+$d_l$-$d_l^c$ for $d_l$≥$d_l^c$. Thus, for 1≤$d_l$≤$d_l^c$ these trees are finitely ramified, and for $d_l^c$<$d_l$≤2 infinitely ramified. The possibility that structures are fractals in l space and compact in r space also is discussed.