But to separate it from crystal formation or some other chemical process is the mutations need to accumulate and have direction.
They only have to accumulate. Accumulation creates a direction.
You made a false distinction. If changes accumulate, then the direction is determined by what is accumulating.
Natural selection is determines the direction of biological evolution. The direction is determined by 'survival of the fittest'. 'Survival' means accumulation. The inheritable variations that survive accumulate.
Complexity can result from the accumulation of random variations even in nonbiological systems. Crystal growth (e.g., snowflakes) is the best known example of a nonbiological process that develops complexity through accumulation. However, the annealing of crystal defects may in some ways be a better example where complexity grows. Individual defects are probably irreproducible. There are many variations on the slip plane.
If a crystal is bombarded with high energy radiation, then it develops point defects on an atomic level. Individual atoms are knocked out of position in the crystal lattice, often leaving nearest neighbors alone. Atomic forces are generally short range compared to the lattice constants. Therefore, a high energy particle can knock two maybe three atoms out of position in the lattice at one time. Hypothetically, the point defect is immortal at absolute zero temperature.
Point defects often form while the crystal is solidifying from a fluid. Note every atom sticks the surface in the exact lattice position. So
Point defects include both vacancies and interstitial atoms. Point defects aren't thermodynamically stable. They represents local valleys in the potential energy of the crystal. However, there is generally a peak in potential that prevents them from recombining right away. Point defects have activation energy that prevents them from instantly disappearing. So point defects have a limited lifetime/
Absolute zero temperature is not achievable by the third law of thermodynamics. Defects move around and interact at finite temperatures. No one has been able to achieve temperatures so low that point defects are stationary. They move around and interact. They destroy each otehr by recombining. They catalyze the destruction of other defects. They combine into extremely complex defects that are often relatively stable.
The result is that crystals anneal. Most of the defects disappear over time. Most are destroyed by other defects. However, some defects combine defects that are more stable than the defects that came before them. Some of the defects are more complex than the ones that came before. In fact, the most stable defects are very complex.
There are many recognizable types of defects. Slip planes look like long lines. Some defects look like long corkscrews, spiraling with an atomic diameter. Some of these defects are stable for temperatures below the temperature at which they formed.
The result is that the crystal anneals at finite temperature. Crystal growers often heat the crystal to reduce the number of defects. However, this never destroys all the defects. The defects that remain become more complex.
The result is that most crystals have complex defects that in quasi equilibrium at some finite temperature. The crystal retains point defects, of course. However, these point defects move around at finite temperatures. Stationary defects tend to be very complex.
Atomic scale defects form at very high temperatures. Vibrations knock atoms out of place. So you can't remove defects entirely by heating them. Cycles of heating and cooling make very complex
Few crystals are perfect at achievable temperatures. A few perfect crystals have been made using very complex technology. However, only crystals made of a single element can be made defect free. For example, perfect crystals of silicon have been manufactured. However, crystals made of more than one element can not be made defect free even with the most elaborate technology.
Minerals (i.e., natural crystals) always have defects. without defects. Defects in a mineral are like fingerprints. Every crystal has its own distinct pattern of defects. Defects on an atomic and molecular scale can be identified by various types of spectroscopy.
Complex defects often determine important properties of that crystal. The tempering process creates very complex defects on a molecular scale. Tempered steel is hard due to its slip plane defects. The hardening due to slip plane defects is comparable to the hardening due to carbon and other elements. Iron crystals without defects and impurities is very soft.
So crystal annealing is a good example of a process where 'random variation' together with 'natural selection' creates unique structures of great complexity. Biological evolution is not the only process that creates complex and irreproducible structures.
I didn't think that was what I was saying. I think I've blurted out my view on it elsewhere in this thread, but I'm being lazy and I'm not going to go look it up. 
