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<<snipe>> ..... but is there a pattern to all of this? Can I guess, for example, what type of fin the offspring of a Twin-fin X + a Speckled Y will have?



Yes, you will figure that out. Each Twin-fin and Speckled breeding will yield the same result.

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Or what type of body?



Same thing with the body type. A shark breed with a groper will always yield the same body type.

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<<More Snipe>>
Also, is there one of each fin-type for each body-type? Or do some body-types not have all the fin-types? Or do ANY of the body-types have all the fin-types?



Every body type can have every fin type. There are two body types and two fin types that can only come from eggs, or by using the strange read liquid. If you have those four fish, you can breed every type of fish in FT.
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The VI