Some CryptoKitties are classified as Fancy cats. Their artwork differs from the standard set of cattributes. After a fancy cat is unlocked/discovered, you can breed your own by combining certain cattributes until the limit is reached. (Exclusive cats like Genesis cannot be reproduced through breeding.)
Fancy Cat Recipes and Limits
DuCat (10,000) = cymric + tongue
ShipCat (2,000)= sphynx + luckystripe + crazy + orangesoda
Dracula (2,000) = laperm + spock + strawberry + wild_1
Mistletoe (2,000) = crazy + oldlace + gerbil
SantaClaws (1,000) = cloudwhite + scarlet + beard + wild_d
PhuZiqaat (1,000) = chartreux + spock + alien + pouty
Stitches (500) = hintomint + swampgreen + seafoam + saycheese
Negato (500) = onyx + henna + wolfgrey + slyboots
Momo-chan (500) = onyx + henna + wolfgrey + sass + bloodred
Earnie (500) = orangesoda + birman + grim + hotrod
MisterPurrfect (1,000) = strawberry + chocolate + wuvme + baddate
YuriCatsuki (250) = elk + tiger + cymric + neckbeard
For information on how to tell if your parent kitties carry the necessary wild gene, see my post on How to Read Your Kitty’s Genome.
There are also add-on cattributes like Elk and Trioculus.
What happens if you breed a cat with all the required traits for TWO fancies? See my post: A DOUBLE Fancy?!