The work of Alan Turing includes a mathematical study of how complexity can arise from nature. It is a biology paper, titled "The Chemical Basis of Morphogenesis" and it describes his theory in something he called a reaction-diffusion system. In it he shows how complexity can spontaneously spring from simplicity.
In essence you create the building blocks of life from the stormy conditions of primordial Earth oceans. Now they are floating around in the mineral-rich oceans, floating in random orientation and moving in more or less random directions, influenced by tidal flow - which is not always uniform. These molecules collide in random orientations. Most of the time, the collisions are passive - but there is this little thing called electrophilic attraction such that it is POSSIBLE for the colliding molecules to stick together chemically - i.e. a chemical reaction. And for small molecules, their virtual surface is COVERED with electrons that can be shared by forming a chemcial bond. That bond is strong enough that the combined molecules stay combined for a while. The more stable the bond, the longer the components stick together.
So now you have these slightly more complex molecules floating around colliding with other molecules... and some of THEM exhibit electrophilic attraction to an active part of the molecule, so THEY react. Here is Nature, bouncing random molecules in random orientation, and SOME few collisions yield greater complexity - because, of course, they are BIGGER now and become easier targets.
So these molecules bounce off of other molecules. Some of the collisions promote increased molecular complexity, others don't. But all this time, for hundreds of millions to a couple of BILLION years, the collisions continue as Nature iterates through the orientation combinations, the moral equivalent of tossing the spaghetti on the wall to see if it sticks. Or of a child playing with Legos to see what will hold together. Iterating through solutions, most of which don't stay together. But some of them do. And it all depends on random collisions of molecules to see what sticks. I went through the math earlier in post #280. You had 4.8 x 10^39 collision possibilities that would be likely to be productive over a time span measured in billions of years.
Let's try something simpler. Do you know how rubies, sapphires, and emeralds form? In solution, chromium oxide molecules collide and become dichromium oxides, then trichromium, etc., forming the start of a crystal that grows layer by layer, driven by the forces implicit in entropy/energy balance. From the simple to the complex. Nature iterating through collision orientations to see what sticks. Sound familiar? See a pattern here?
