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Diatoms and valve morphogenesis are a combination of static structure formation at specific time junctures and a dynamic progression to the formation of the vegetative cell. As static structures, diatoms have high symmetry, termed uncanny symmetry. As selforganizing siliceous structures, they are some of the most stable static structures. Entropy as an ensemble measure [2.84] is instrumental in measuring of silica-deposited dynamics during valve formation that lead to the various regularly created geometric patterns defining species-specific valve surfaces.

The dynamical process from a more to less chaotic unstable state may be a characterization of self-organization. In the valve formation process, self-organization is the recovery from a chaotic unstable state, even though the chaotic state could be construed to be “normal.” Symmetry is a reflection of these states. In contrast, abnormally developed valves could be construed to be in a higher “abnormal” chaotic state, and stress during valve formation is evidenced by the resultant vegetative cell and its increasingly asymmetry state. Self-organization as the appearance of new structures may be a transition from a more chaotic, unordered to less chaotic, more ordered symmetry state, or vice versa in the case of a final abnormal symmetry state. In this way, equilibrium states during non-linear dissipative fluctuations in a dynamical system may end up being the most chaotic states [2.71].

The picture that symmetry and its relation to stability exhibits during morphogenesis is not straight-forward. In fact, no quantitative generalized overall framework for evolutionary dynamics, including stability of structural inheritance or structural integrity during reproduction for changing environmental conditions, exists with respect to diatom morphogenesis [2.131]. From our study, we give a speculative understanding and interpretation of our results on symmetry and stability as they pertain to the three major steps of centric diatom morphogenesis [2.126].

Figure 2.25 Average sequence of 24 simulated valve formation steps of symmetry for eight centric diatom taxa. Symmetry increases exponentially from the annulus to the completed valve.

Overall, symmetry increased over the valve formation simulation with highest symmetry at the finished vegetative valve (Figure 2.19). The basal layer that forms from silica deposition horizontally during the first major step of diatom valve morphogenesis, starting with the annulus, is roughly covered by the first 8 of 24 “stages” of simulation (Figure 2.18). Symmetry with the lowest values occurring at approximately the same value (Figure 2.25). For roughly “stages” 9–16 representing the second major step, vertical silica deposition is represented by the changing luminosity of pixels in the central area of the images as the indication of the formation of rays and areolae emerges (Figure 2.18). Symmetry changes become more evident, going from low to higher symmetry, yet still within a small range (Figure 2.25). For the final major step, horizontal silica deposition is represented by even more changes in pixel luminosity over the valve face in “stages” 17 to 24 where indications of the formation of cribra going toward the valve margin is present (Figure 2.18). Symmetry changes are highest in these “stages”, representing completion of silica deposition of the valve (Figure 2.25). The valve forms present during the three major valve formation steps may be viewed as symmetries functioning as silica depositional ensembles changing in direction and magnitude (horizontally to vertically to horizontally again) on the valve face. This dynamical system operates at equilibrium with exponentially changing symmetry occurring via chaotic instability during valve formation.