I just bought some Koi fish for my pond. These are Amur carp fish with different colored variants.
They are amazing fish i have heard the live up to 30 years or something like that 
The koi are popular in Japan where they recognize many varieties.
Do you know how old was the longest living koi fish?
I do not. But the different Koi fish are distinguished by their scalation, patterning, and coloration.
that is really interesting, what are some colors koi fish 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
throughout Japan. From this original handful of koi, all other Nishikigoi varieties were bred, with the exception of the Ogon variety (single-colored, metallic koi), which was developed relatively recently. 
The hobby of keeping koi eventually spread worldwide. They are now sold in many pet aquarium shops, with higher-quality fish available from specialist dealers. The collection of koi throughout the years has become quite the social hobby for many who have ponds. It is also common for hobbyists who are passionate about their koi