CryptoKitties mixGenes Function

Kai wrote up an excellent explanation of how the 256 bit gene number breaks down. You can find that article here. You should understand those concepts before going on.

The mixGenes function gets called when you breed two cats. This is how the baby’s genes are calculated. You can find the byte code in the smart contract at https://etherscan.io/address/0xf97e0a5b616dffc913e72455fde9ea8bbe946a2b#code. I spent the time stepping through it to understand exactly what was going on. Here’s the pseudocode to start. It’s pretty dense but an explanation will follow.

def mixGenes(mGenes[48], sGenes[48], babyGenes[48]):
  # PARENT GENE SWAPPING
  for (i = 0; i < 12; i++):
    index = 4 * i
    for (j = 3; j > 0; j--):
      if random() < 0.25:
        swap(mGenes, index+j, index+j-1)
      if random() < 0.25:
        swap(sGenes, index+j, index+j-1)
  # BABY GENES
  for (i = 0; i < 48; i++):
    mutation = 0
    # CHECK MUTATION
    if i % 4 == 0:
      gene1 = mGene[i]
      gene2 = sGene[i]
      if gene1 > gene2:
        gene1, gene2 = gene2, gene1
      if (gene2 - gene1) == 1 and iseven(gene1):
        probability = 0.25
        if gene1 > 23:
          probability /= 2
        if random() < probability:
          mutation = (gene1 / 2) + 16
    # GIVE BABY GENES
    if mutation:
      baby[i] = mutation
    else:
      if random() < 0.5:
        babyGenes[i] = mGene[i]
      else:
        babyGenes[i] = sGene[i]

It’s a bit dense so we’ll go through it one section at a time.

First up is the parent gene swapping. This is how you can get your recessive genes into the dominant slot. The best explanation is by example. Let’s say you have a kitty with traits (D, R1, R2, R3), that’s dominant, recessive1, recessive2, and recessive3. What the parent gene swapping does is with 25% chance it will swap R3 and R2, then R2 with R1, then R1 with D. Keep in mind that these happen one after the other, so you could end up swapping R3 down to R2, then to R1, then to D all in one go. This is extremely unlikely. Like 1.5% unlikely. Don’t expect your R3 genes to become dominant in one step.

Next up is the mutation section. This part is probably the most difficult to follow. First, understand that this only happens after the gene swapping above. So you may have your genes in different places by the time this happens. The first line if i % 4 == 0 makes sure we only mutate on the dominant gene. Next we swap the genes so that the higher valued gene is gene2. Now we can test the precondition for a mutation if (gene2 — gene1) == 1 and iseven(gene1). Yes, that’s right, you not only need specific combinations of genes, but you also need the value to be even. Keep in mind here that Kai values are +1 from their binary. All the math here should be done on the binary value. Once the precondition passes, we do a mutation with 25% probability if the value is less then 23, and half of that otherwise. And the mutation is just as predictable, mutation = (gene1 / 2) + 16.

After that the last section is easy. Give your baby some genes! If there was a mutation, they get that. Otherwise, there’s a 50% chance for each parent. Pretty easy stuff there.

I hope this helps in choosing your kitties. With a bit of math you can easily understand the probability of getting traits in your new kitties.

If you found this useful, consider donating some eth so I can actually afford some low gen kitties. 0x9de0132bd201963082b80a6774719f8bfbd52b32