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Addballs are commonly used to make tail shapes that differ from the typical raised tail without having them break when animating. Most of the time this works fine, but a bug can appear when you breed a pet with an addball tail to a pet with a normal tail and the resulting offspring has two tails, one from each parent. As an example, here is a labrador I hexed to have an addball tail. I omitted the existing tail balls and built up a long, lizardlike tail instead. A tail like this would animate badly if made from the original tail balls, so addballs are ideal.
I then bred her with a regular unhexed great dane from the adoption center:
Among the resulting offspring was this dog, who has both the hexed tail from her mother and the normal tail from her father:
Note that this bug doesn't always happen - I had to breed this couple a few times before this happened, and most of the offspring were either tailless or had the normal tail. So you can safely cross addball/natural tailed petz and most of the time you wil be ok, but this bug can still show up. But why does it happen and what can you do about it? It's to do with the way the game mixes the parent petz' body shapes to create a baby.
A petz' body is broken down into distinct areas called groups (which is what the group number refers to if you're editing the Ballz Info or Addball sections in LNZ Pro). The head is a group, the body another, and so on. When two petz breed, the game combines different groups from each parent to create offspring who are a mixture of the two. Critical to this bug, the torso ballz are considered part of one group, and the tail ballz another. Our double tailed dog inherited the hexed labrador torso shape from her mother, and the normal great dane tail shape from her father.
But how does inheriting the hexed lab torso shape give her the hexed lab tail? You can see the reason why if you look at the tail addballz for the hexed lab file in LNZ Pro. Specifically notice the first column, which is the base ball:
tail addballz with base column circled
It's 49, which is the butt ball (note: if this was catz, the butt ball would be 3). In both dogz and catz, the butt is part of the torso group. Because there is nothing to tell the game what group these addballz are part of, it thinks they're part of the torso and they inherit as such. Remember how earlier I mentioned some of the other offspring from this pair were tailless? That is because they inherited the mother's tail group, and from the game's perspective she has no tail as all her tail ballz are omitted. So, to avoid both the double tail and tailless offspring bugs, we have to tell the game that these addballz belong to the tail group, and not the torso.
The way to do this is to base the addball tail on an existing tail ball. A common way to do this is to omit all the normal tail ballz except tail1, the ball closest to the body (note: in dogz tail1 is ball 57, in catz it's 43). Because your tail addballz are now based on a ball in the tail group, they will inherit as a tail. This also has the advantage that you will have some movement in your tail instead of a completely static appendage. My spotted hyena breedfile works like this, having a drop tail based on tail1 to allow it to move but point downwards.