The GreenLab model describes plant organogenetic development and photosynthetic functioning by a discrete dynamical system. The time step is called the growth cycle and corresponds to the duration between the appearances of new organs. The GreenLab mathematical formalism allows studies of the system behavior. From the assumption that tree development strongly depends on the amount of available biomass, a new version of the model has been developed to take into account interactions between organogenesis and photosynthesis. The biomass produced is dynamically shared between organs according to a proportional allocation model: each organ has a given sink and the sum of all sinks is the plant “demand”. To implement interactions in the model, the ratio of available biomass divided by plant demand has been chosen as the key variable to control plant development. For example, at a given growth cycle, branches or fruits only appear if the ratio exceeds a particular threshold that is a parameter of the model. In this paper, we present how the dynamical evolution of this ratio can naturally induce rhythm apparition in the plant development. Two main phenomena are particularly studied: fructification and branching. After a brief presentation of the model, numerical simulations will illustrate how functioning can generate rhythmic organogenetic phenomena: variations of the ratio of biomass divided by demand around the threshold value create an alternation between cycles with great and low fruit productions (such a process is observed on beech trees). Likewise, periodical branching patterns are generated. Then, a mathematical study of the system will be presented. Conditions on the appearance of such rhythms are determined as functions of the plant endogenous parameters and of environmental conditions. This model offers great perspectives in terms of tree behavior representation and study. It should help us understand some hidden mechanisms of tree growth.