Evolution, Mathematics, Autopoiesis and Living machines

Lately I've been looking at issues regarding what is the criteria to describe living things? and why physical phenomena take the form they do?

The theory of evolution by natural selection was first put forth in detail in Charles Darwin's 1859 book "On the Origin of Species". In the 1930s, Darwinian natural selection was combined with Mendelian inheritance to form the modern evolutionary synthesis. With its enormous explanatory and predictive power, this theory has become the central organizing principle of modern biology, providing a unifying explanation for the diversity of life on Earth.

Obviously, "On Growth and Form" the D'arcy Thompson's original book written in 1917, had to be revisited. He looks at the way things grow and the shape they take. In the chapter "On the theory of transformations." He explored the degree to which differences in the forms of related animals could be described by means of relatively simple mathematical transformations. The central thesis of "On Growth and Form" is that biologists of his day overemphasized the role of evolution, and underemphasized the roles of physical laws and mechanics, as determinants of the form and structure of living organisms.
Now, Autopoiesis literally means "auto (self)-creation" from the Greek, and expresses a fundamental dialect between structure and function. The term was originally introduced by Chilean biologists Humberto Maturana and Francisco Varela in 1973. The term autopoiesis was originally conceived as an attempt to characterize the nature of living systems. A canonical example of an autopoietic system is the biological cell. This body of theory concerns the dynamics of living systems, purporting to answer the question "what is the characteristic organization of living systems?" The process of Autopoiesis lies at the heart of the answer. Autopoiesis (the process) is defined through a definition of 'living machines'. (to be continued)