Well I must say I don't know anything about modeling ligand-proteins interactions but I assume that the results obtained are general and not exact when trying to determine the reaction of a specific protein as observed in nature. The fact that the results are generally accurate simply indicate that the inputs were generally similar too. (Both use generally similar environments and ligand-proteins as inputs)
I'm sure if the environmental variables in those experiments briefly shot up to include temperatures near 1000 degrees, the protein interactions would not be the same as when the temperature were assumed to be around 20 to 100 degrees.
Theoretically the end result would still be four. In reality if might be 3.005 or 4.00000000001.
Are you sure? Can you realistically determine that with a real life experiment with the exact same conditions every time? I don't think you can, you'd have to take into account things we can't even think of yet(like what would the influence of dark matter, which we know almost nothing about, be on that experiment? Can it be assumed that it would not have an influence?).
In my line of work(not scientific but we use very complex and smart software) we sometimes have to do fluid simulations where the software we use takes millions(or billions, depending on how realistic you want the result to be and how much CPU's and time you've got access to) of separate particles, calculated as vertex points in space, with individual vector directions which interacts with set forces and with each others forces and set masses in order to simulate fluid interactions.
Now I realize this is just a approximate simulation on a PC but the simulations results, like your ink example(yes we've actually done those and yes its a nightmare

) are ALWAYS identical,
except when you add some variation in particle mass, gravity, initial states, inertia and force strength and vector variations.
The results for the machines will be similar in a general sense but not in an exact way. If you put little mines randomly on the bottom of the bathtub, the fate of a particular machine can change drastically depending on where exactly it lands. Its chances of survival will be determined by specific initial states.
The colouring will appear to spread in a stochastic way to us simply because we don't have the ability to take every variable in reality into consideration nor the ability to recreate it for experimental purposes.
If the initial variable states for the colouring were identical I believe the results would be identical too. Other wise it would mean that 2+2 <> 4.
Approximate inputs would give approximate results wouldn't it? Thus any assumptions of
complete accuracy may simply be wishful thinking.
Yes?
I can't comment on genetic algorithmic search techniques and such, I do not have the background knowledge to discuss it.
What I am trying to say though is that these things are determined by basically extremely complex equations with extremely complex and seeming obscure variable inputs. But they still follow mathematical laws.
And if we are not able to take every single input variable into account as it relates to reality, it is not accurate to say that the results of a calculation would be the same regardless of the inputs. They may be approximately the same, but approximate inputs added to another equation may result in a very different results, which to me, indicate that there is no plan. Except if you assume the mathematical laws of the universe to be the plan. But that would be an assumption.