[uh_uh]

Let's take human DNA as an example. It contains 3.2B GTCA base pairs. This gives rise to 4^3.2B possible combos. It's just not possible to navigate this space blindly. There is not enough atoms in the universe to do that. It is known that there is bias in what mutations are favoured.

[PaulDavisThe1st]

Only a tiny percentage (around 1%) of the DNA in chromosomes codes for proteins.

And yes, certain mutations are favored precisely because of the chemistry constraints (an extremely basic one is which base pair changes actually alter the resulting protein; a more sophisticated one is which amino acid changes alter the physical functionality of the protein).

[uplifter]

Of course there is bias, the bias is provided by the natural environment where the organisms coded by the genome must thrive or die. The bias is applied after the mutation occurs, but the mutations themselves are random, or nearly so. Probably there is some differential rate between the likelihood of each of the four base pairs to mutate into each of the others, but I would guess its nearly parity, because that would probably be close to optimal (though that depends on the details of the genetic coding scheme, ie the triplet code that translates nucleotide triples into amino acid codons).

[uh_uh]

I don't think this is true at all. There are multiple sources talking about how the mutation rate is context-dependent.

[Supermancho]

There are multiple constraints that I can immediately identify. Maximal temperature extremes, barometric pressure, atmospheric/substrate compositions, etc. The bias is inherent to the history of the planet Earth and the gradients present across that time and space. I'd say it's highly constrained.