**3.1 The "cauliflower effect" and its links with hydrological features**

The series of processes from the cause generating a cauliflower form is complex. One might assume that the underlying rules for the cauliflower growth are simple, even if the form is of great complexity [43]. But the crucial phenomenon that ultimately leads to much of the structure is that at the tip of a stem is possible for new stems, to form and branch off. In the simple cases, these new stems are in essence just smaller copies of the original stem. With this setup, the branching succession can be represented by steps in the evolution of a neighbor-independent substitution system. The cauliflower finally presents an unusual phyllotaxis, with a multitude of spirals nested over a wide range of scales. This self-similar organization culminates in the Romanesco cultivar, where the spirals appear in relief due to their conical shape at all scales, a geometrical feature conferring the whole curd a marked fractal-like aspect [43].

Similarities can be found by comparing forms of cauliflower and hierarchical river organization: without geological or lithological constraints, a stream river branching progress through scales [44], and if the distance before the stream appears is

determined by the rates of production or the erosive capacity of waters, a minimum area is needed for elementary catchments [45]. The layout of the network becomes fundamental considering the path and transit time, from the source to the outlet. The *width function* created by [46] has permitted consideration of the number of hydrological links located at equal distances from the outlet [46], thus taking into account the network and the surfaces within a given watershed form. This function remains today one of the most relevant tools, to link the shape of a basin and its hydrographic network, to the hydrological response resulting from this organization [25, 27], even if numerous works have improved the calculation and the method of extraction of this function, by associating the slopes. A structurally well-organized network finally presents, without external constraints, a form nearest to those of a cauliflower: it represents a homothetic phenomenon, with a minimal dispersion of energy, which reminds the "self-organized critical systems" [47]. But the global catchment form can be hidden on the global scale. Then, we create a specific model to measure this effect.
