Earth's systems, in manifold ways, feature characteristic rhythmic patterns such as banded formations, layered and folded structures, diapirs or cockade ores that can range from just microns, and even sub-microns, up to kilometers in scale. This subject has been examined from a thermochemical/ thermomechanical perspective since time immemorial. 

Likewise, the physical perspective was for a long time limited to characterizing continuous changes in closed systems. The concept of self-organization (I. Prigogine, 1977), however, makes it possible to describe discontinuities as spontaneous sequential 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. To enable spontaneous structure/texture formation, the open systems should be far from thermodynamic equilibrium.

Looking at closed systems, changes inevitably cause an increase in complexity and disorder (increase in entropy). In contrast, the concept of self-organization in open systems lays the foundation for changes paired with simultaneously increasing order and complexity by means of entropy export and energy dissipation in which phase transitions play an essential role. Precipitate patterns facilitated by solute reactions have been discussed in detail since the 1980s (P. Ortoleva, 1982). Another characteristic of open systems, the scale invariance, is formulated by H. Haken 1978 with his synergetics concept.

As the Earth´s system in general is considered as an open system comprising 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 Earth´s universe of processes and remarkable rocks.

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 mineral formation, the findings of experimental, theoretical, and numerical analyses will be looked at in detail unveiling access to desired minerals and valuable mineral resources. Finally, generalized results will be considered for future investigation.