Are there hybrid (discrete-continuous) combinatorial structures, which can grow (develop) according to the discrete and continuous rules at the same time: i.e. some part for some time can grow according to some selection of discrete rules and then the new structures may further develop (again for some time) according the the continuous rules.
Of course, one can say that continuous rules always generalize the discrete rules, but discrete rules are more or less the compact form of the continuous rules and that is why it can be beneficial to take them into account into computation.
This may be question about existence of hybrid fractals or hybrid combinatorial structures: continuous parts of such structures are specified in detailed form and their geometric form (length, exact dimensions) are significant, but the symbolic part are specified up to morphisms (i.e. only shape/topology/symbolic content is relevant; numeric measures of distances in concrete representation are irrelevant).
It is said, that combinatorial species (https://en.wikipedia.org/wiki/Combinatorial_species) use generating functions to describe the discrete structures. Maybe combination of such generating functions with the usual functions (e.g. as solutions from the differential equations of evolution) can describe the hybrid combinatorial structures? Have someone tried to do this? Or I am the first one to see the need for such structures?
From the other side - there is hybrid logic by Platzer (http://symbolaris.com/) but it describes the continuous/hybrid evolution of the predetermined system and does not describe the combinatorial growth of such system.
We can see the words in some formal language as the combinatorial objects that are generated according to the rules of the formal grammar. Parsing provides the method of recognition and understanding of such combinatorial objects (words). But we can consider real world concepts/physical objects as combinatorial objects that emerge from the physical primitives/primitive shapes - some steps of this evolution changes the topology/essence, some steps changes only the physical dimensions. If we have control over such combinatorial structures, then we can develop parsing algorithms and use them for recognition/understanding/semantic understanding of multimedia data. Robot motion grammar (http://www.roboticsproceedings.org/rss07/p07.pdf) some step in this direction, but my proposal is the generalization of that. My proposal can form the framework for unification or all semantic parsing algorithms, but some mathematical bases is needed for that.
Any terms, hints are welcome. I can research the question further myself if any tread is provided.
Of course, I googled and Google gave nothing, maybe there are such objects but they are named differently?