I have apond in my back yard and I put some Koi in it. That's just a group of colored variants of the Amur carp. It's nice. 
Koi fish are beautiful, where did you get them?
A local pet place. I like how the varieites are differintiated by coloration, pattern and scalation,
Oh I see, what kind of patterns and colors do they normally have?
Asia may be necessary, as the genetic variations do not fully match the currently recognized species pattern, with one study of mtDNA suggesting that koi are close to the Southeast Asian carp, but not necessarily the Chinese.
Varieties.
Koi varieties are distinguished by coloration, patterning, and scalation. Some of the major colors are white, black, red, yellow, blue, and cream. Although the possible colors are virtually limitless, breeders have identified and named a number of specific categories. The most notable category is
Koi
Koi is an informal group of the colored variants of "C. carpio". Several varieties are recognized by the Japanese. Koi varieties are distinguished by coloration, patterning, and scalation. Some of the major colors are white, black, red, orange, yellow, blue, and cream. The most popular category of koi is the "Gosanke", which is made up of the "Kohaku", "Taisho Sanshoku", and "Showa Sanshoku" varieties.
History.
Carp are a large