Complex systems became understandable due to the discovery that there exist no other relationships than complementation or supplementation in nature.

Therefore there exist no other relationships between elements that integrate the unified field of a complex adaptive system than complementation or supplementation.

The purpose, the conservation function and the active function of a concept are integrated by logical rules which sustain their unity.

While the purpose and the active function are sustained by the supplementation law, the purpose and the conservation function are integrated by the complementation law.

Supplementation Law

It is a relation between elements with redundant purposes and active functions, having a different energy conservation element. One of the elements has a superior “myth” that challenges the evolution of reality.

Complementation Law

It is an interdependent relation between two elements, actions or ideas. Each one of these elements has what the other element requires and they both have a homologous energy conservation element.

Levels of supplementation and complementation

There are three different levels of complementation and supplementation integrated in a unified field / object: Essential, Operational and Functional.

Supplementation

Supplementation puts the purpose into action and fosters its evolution. The purpose of supplementation is to ensure the operation and functionality to achieve a purpose, trying at the same time to upgrade the purpose increasing the added value and its field of possibilities.

Operational supplementation ensures operation while intending to increase the value added. Functional supplementation ensures functionality and intends to increase the field of possibilities of the purpose.

Essential supplementation integrates both operational and functional supplementation in their oneness.

The conflict between the supplementation and the purpose it supplements drives towards evolution if it poses a superior value which implies a superior generation of value. When it fosters a superior level of value appropriation it generates a short term growth but a long term involution.

Complementation

Complements sustain the purpose to avoid the entropy produced by the action. Complementation increases the reliability and functionality of a purpose while ensuring operational and functional cooperation.

Operational Complementation increases reliability and operational cooperation while Functional Complementation increases functionality and functional cooperation.

Complementation needs to achieve a minimum threshold of energy in order to become functional. Complementation becomes functional when it becomes a necessary and not only convenient added value. This level is achieved when the there is an actual essential complementation.

Complementation in nature might be asymmetric, symmetric or parasitic. Evolutionary complementation requires the integration of asymmetric complementation with a negative slope with symmetric complementation. Parasitic complementation naturally generates the involution of the unified field where it is installed.