Figure 2
This image shows the generalized French Flag model. A cell pattern can be considered as a string in the alphabet (red, blue, or green). This pattern can be produced by chaotic dynamics as follows. Let u be a vector of morphogen’s concentrations, which lies in morphogen concentration space \({{\mathscr {U}}}\). Suppose that this space is split into three subdomains \({{\mathscr {U}}}_j\), \(j=1,2,3\). If \(u \in {{\mathscr {U}}}_1\), morphogen concentrations induce differentiation into a red cell, and if \(u \in {\mathscr U}_2\), \(u \in {{\mathscr {U}}}_3\) then one has blue and green cells, respectively. When u-dynamics is governed by a chaotic (noisy) system, there exist time moments \(t_1, t_2, ..., t_m\) such that the u states enter for \({{\mathscr {U}}}_j\) at certain time moments: there exist \(t, t+\Delta T, ..., t+m \Delta T\) such that state \(u(t+j\Delta t)\) lies in the corresponding domain \({\mathscr U}_{a_j}\). In the considered case, we have a string \(\textbf{a}=2313322112\). It is important that the choice of chaotic dynamics and specific choice of partition \({{\mathscr {U}}}_j\) is not essential. Any stochastic (chaotic) ergodic dynamics is capable, earlier or later, to generate the needed string.
