$T2$ that are driving cell disappearance in foam evolution (see Fig.1 and [@dubertret]). Moreover, the cells in grain boundaries, which are truncated squares, almost meet at four-corner vertices, the critical point for $T1$. Thus, phyllotaxis is a topologically stable but malleable arrangement.

The grain boundaries (defect rings) constitute specific layers, a concept in (disordered) foams that uses the notion of topological equi-distance [@oguey].

Layers and defect inclusions in foam
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Layers are best illustrated in Fig.\[fg3\], taken from [@aste]. The nearest neighbors to an $n$-sided cell $\mu = 0$ are $n$ cells at distance $1$, thereby defining topological distance. They constitute layer $\mu =1$. And so on, for layers $\mu = 2,3, \dots$. Three defect inclusions (shaded) appear in layer $3$. They are neighbor cells to layer $2$ but not to any cell of layer $4$.

A foam (space-filling cellular complex) can be decomposed into successive layers $\mu-1,\mu,\mu+1,\cdots$ going up (or outwards), or $\mu+1,\mu,\mu-1,\cdots$ going down (inwards). The cells of the layer are all at the same topological distance to an origin layer $\mu=1$, going up, or $\mu=\mu_{max}$ going down. [@oguey]. In phyllotaxis, the layers are naturally anchored on the defect rings, so that the origin layer is specified only 