Geosystems especially in the Earth’s crust often feature rhythmic patterns such as banded formations, layered and folded structures, diapirs or cockade ores that can cover scales from just microns, and even sub-microns, up to several kilometers. This subject has been examined from a thermochemical-mechanical perspective since times. 

As well for a long time, physics was limited to characterizing continuous changes in closed systems. The concept of self-organization (I. Prigogine, 1977), however, enables to describe discontinuities as sequential spontaneous structure/texture formation. For this reason, the earlier approach in closed systems with given boundary conditions of existing "ideal gases" is abandoned and instead open systems with distributed components and properties (W. Ebeling, 1976) as well as available free energy are introduced. For allowing spontaneous structure/texture formation, the open systems should be far from thermodynamic equilibrium.

In closed systems, changes inevitably cause an increase in complexity and disorder (increase in entropy). Contrarily, the concept of self-organization in open systems lays the foundation for changes going together with increasing order and complexity at the same time, i.e. by means of export of entropy and energy dissipation. Here, phase transitions play an essential role. Precipitate patterns mediated by solute reactions have been discussed in detail since the 1980s (P. Ortoleva, 1982).  As a further characteristic of open systems, the scale invariance is formulated by H. Haken 1978 with his synergetics concept.

As the earth system is considered as an open system including geochemical processes and geomaterials of all scales that changes because of the supply and withdrawal of energy, ordered structures and patterns are typical features in geological systems.

In this talk, radiolarite, malachite, reef limestone and banded iron-manganese deposits will be addressed as illustrating examples. Using the example of a recent early diagenetic new mineral formation, the findings of experimental, theoretical, and numerical analyses will be discussed. Finally, generalized results will be considered for future investigation.