I have started collecting different variations of sylesties and breeding them, but how do you make a mutation or trait pass down to the offspring? Example, a Ryori has ethereal armor and the other ryori has punk wings, how do I make those go into the offspring, or is it by chance? Thanks in advance!

it's punnett square genetics, so when breeding it takes each of the separate traits, and randomly selects one of the two letters from each of the parents, with dominance being N>A>B>C>D>E>etc. down the alphabet (with N being Nothing)

So if you had a Ryori with just Ethereal armor:


And a ryori with just Cyberpunk wings


You'd get a no-vis offspring with the genetics

Gene One: (NN) None
Gene Two: (NN) None
Gene Three: (NN) None
Mutation One: (NA) Ethereal Armor
Mutation Two: (NH) Cyberpunk Wings
Mutation Three: (NN) None

Because
parent one is passing down M1 (AA)/M2 (NN) and
parent two is passing down M1 (NN)/M2 (HH),
(unless one of the parents was untested and had a carried in the either M1 or M2 that wasn't taken into account)
The Offspring could potentially have children of its own who showed the traits, depending on what it was bred with, though.

So if I took...

genetics:
Gene One: (NB) Marbled
Gene Two: (NA) Kitsune
Gene Three: (AA) Nebula
Mutation One: (BB) Ghostly Wraps
Mutation Two: (AB) Ethereal Ribbons
Mutation Three: (NB) Mystic Mask

and

genetics:
Gene One: (NN) None
Gene Two: (AA) Kitsune
Gene Three: (NB) Lucky Runes
Mutation One: (NC) Petal Wreath
Mutation Two: (HH) Cyberpunk Wings
Mutation Three: (BB) Mystic Mask

Offspring could be any combo of:

Gene One: (NN) None or (NB) Marbled
Gene Two: (NA) Kitsune or (AA) Kitsune
Gene Three: (NA) Nebula or (AB) Nebula
Mutation One: (NB) Ghostly Wraps or (BC) Ghostly Wraps
Mutation Two: (AH) Ethereal Ribbons or (BH) Wings of Illusion
Mutation Three: (NB) Mystic Mask or (BB) Mystic Mask

Examples:

Ah, okay, that makes way more sense! Thank you for your help!