Despite the universality of branching patterns in marine modular colonial organisms, there is neither a clear explanation about the growth of their branching forms nor an understanding of how these organisms conserve their shape during development. This study develops a model of branching and colony growth using parameters and variables related to actual modular structures (e.g., branches) in Caribbean gorgonian corals (Cnidaria). Gorgonians exhibiting treelike networks branch subapically, creating hierarchical mother-daughter relationships among branches. We modeled both the intrinsic subapical branching along with an ecological-physiological limit to growth or maximum number of mother branches (k). Shape is preserved by maintaining a constant ratio (c) between the total number of branches and the mother branches. The size frequency distribution of mother branches follows a scaling power law suggesting self-organized criticality. Differences in branching among species with the same k values are determined by r (branching rate) and c. Species with r<r/2 or c>r>0). Ecological/physiological constraints limit growth without altering colony form or the interaction between r and c. The model described the branching dynamics giving the form to colonies and how colony growth declines over time without altering the branching pattern. This model provides a theoretical basis to study branching as a simple function of the number of branches independently of ordering- and bifurcation-based schemes.

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Considering that there are many alternatives in the literature for composing groups in collaborative learning contexts, we present a proposal that exhibits several features. First, and from the operational point of view, our proposal is highly flexible because i) it allows for several group sizes and an arbitrary array of grouping attributes, and ii) it may be easily adapted to consider several homogeneity/heterogeneity criteria. Second, and from the algorithmic point of view, it combines the best of two apparently opposite worlds: it uses a local brute-force search within an iterative process guided by a randomized heuristic criterion. Thus, this approach is still Non-Polynomic (NP) but in terms of the size of the groups, whereas is Polynomic (P) in terms of the number of students. Third, the experiments with several datasets, with student numbers varying from 20 to 3500, demonstrate reasonable performance and running times for this approach. We contrasted these times with those reported in 19 related works and, first taking into account certain considerations, we found that ours were lower in most cases. Nevertheless, and as the fourth feature, we make available both the datasets and the source code to allow for more objective comparisons of approaches, including our own.