Complexity and order in chemical and biological systems

The complexity of structurally defined objects in the chemical and biological context is calculated using a previously defined formalism. Structural complexity is defined as the minimal number of numerical and compositional specifications needed to describe the ordered features of an object . The formalism is applied to a set of simple one to four atomic molecules, incl. H₂, HC1, H₂O and H₂O₂. H₂O₂ is shown to be the prototype of partially ordered systems. Order is defined as the ratio of the ordered to the total coordinates of an object or sequence. Ordered coordinates are discernible from non-ordered ones by a reproducibility criterion proposed. Partial order is the dominant feature in most bio- and man-made systems so that the proposed formalism is capable of treating such systems. This is demonstrated in the last part, where the formalism is applied to a biostructure, the wing eyespot patterns of an African butterfly B. anynana, and is shown to correctly predict the number of genes specifying that structure.