I. INTRODUCTION The building blocks of mathematical morphogenesis were put several decades ago in the seminal works of Thompson [1] and Turing [2]. A particularly relevant problem in this context is the examination of the properties relating to the architecture of cell colonies, as already noted and investigated by Eden [3, 4]. At some basic underlying level, one could say that Turing and Eden shared the goal of understanding how a macroscopic structure, in particular one breaking the initial homogeneity, could arise out of a multiplicity of simple interactions. In the introduction of [2] one can read Turing thoughts on how a structure composed by randomly and isotropically proliferating cells could or could not break the initial spherical symmetry. But then his approach moved to the use of reaction–diffusion equations and to the search of a deterministic mechanism, the currently well known Turing instability, able to give rise to pattern formation. On the other hand, Eden focused his interest on the evolution of a pure growth process. He concentrated on a probabilistic abstraction of a developing cell colony and studied stochastic symmetry breaking concomitant to growth. In particular, Eden studied the architecture of a lattice cell colony to which new cells were added following certain probabilistic rules. The objective was determining the asymptotic colony profile. If the growth rules are isotropic then the realizations of the growth process are either spherically symmetric or this spherical symmetry is broken by means of long range fluctuations. These sorts of discrete models are usually studied using continuum equations for ease of analytical treatment [5, 6]. While most of these developments have been carried out for systems in which there is an external input of mass, the universality of the surface fluctuations is expected to remain unchanged when the origin of mass appearance is internal. In fact, the Eden model in a strip geometry has been satisfactorily analyzed within the classical theoretical framework [7]. And, as we already have mentioned, this model was introduced as a probabilistic abstraction of a proliferating cell colony. So we expect our results to hold independently of the internal or external origin of mass input into the system. This will be so at least in those cases in which the growing radial interface can be described as a Monge patch in spherical coordinates. Growing clusters as the ones generated by diffusion– limited aggregation processes yield more complex structures that cannot be described in such simple terms, and thus fall beyond the scope of the present approach. 2