The coloration and patterns of a Koi are in many cases, the thing that attracts people into the hobby of Koi keeping. These same two factors are also very important in determining the quality and therefore value of any particular fish.
Yet our understanding of fish and, particularly Koi, coloration is still and inexact science, which is plagued by theories, old wives tales and relatively few facts.
My aim here is to provide an overview Kai coloration and in doing so help to explain some of the mysterious changes you may have noticed in your own fish.
All of the colors we see on our Kai are a mixture of these components. For example orange is a combination of red and yellow chromataphores; brown is a mixture of black and yellow and red is just the red chromataphores. If there are no chromataphores present the Koi will appear white due to the irridocytes However, the position of the irridocytes within the skin affects its reflective properties. If they are on the surface of the scales the Kai will have a silvery appearance. If they are in the lower layers of the skin the fish will have a mat color.
In certain cases, the irridocytes can combine with the chromataphores to produce reflective colors (e.g. gold on the surface). Blue is an unusual color in that it is a result of deep lying black pigment with irridocytes in the middle of layers of the skin. The irriclocytes interfere with the light to give a blue color.
If color foods are not given to your Koi, the chromatophores would not be filled with pigment and the Koi will look pale or poorly colored. This can result in a Kai of high potential quality only looking mediocre. Feeding a color food would greatly enhance the appearance of such a Kai - but could not make a poor Kai great.
When the chromataphores are filled with pigment, the excess is passed through the Koi in the feces. It is possible to get white areas of the koi becoming pink due to a temporary build up of Erythrin. This pigment is not in a chromataphores and will quickly disappear as soon as the amount of color food given is reduced.
In some varieties (e.g. Sanke and Showa) it is common for the pattern to change considerably as the fish grows due to the surface color fragmenting and revealing a deeper different color. When your Koi become very old they tend to become paler and in some cases turn white. This is the equivalent of our hair turning gray and cannot be reversed.
Water Quality - Different water quality conditions can have a major impact on the coloration of the Koi. Raised levels of pollutants (e.g. ammonia, nitrite or nitrate) will cause the pigment to contract, resulting in the Koi losing its color. pH and hardness affect coloration differently, red pigment tends to spread in softer, more acidic water, whereas black pigment spreads in harder more alkaline water and vice versa.
Background Color - Although it is difficult to merge into the background when you are a red and white Koi, they do try to do so. Against a pale background the Koi contract the pigment to make themselves as, pale as possible. The opposite occurs when the Koi is next to a dark background, which is why blue vats are used at Koi shows to ensure each Koi looks at its best.
Treatments - Salt is often added to Koi ponds as a treatment or to control nitrite toxicity, however, it causes the pigment to concentrate resulting in poorer coloration. The same is true for antibiotics, whether added to the water or injected and malachite green based remedies.
Algae - Koi (and goldfish) which have lived in an algae rich, green pond often appear intensely colored due to the color pigment spreading in the chromataphores. This effect can be recreated without the "green water' by using Tetra Pond Koi Vital.
Temperature - At high summer temperatures pigments contract; at cool autumn and winter values they expand resulting in the koi looking at their best in the cooler months of the year.
This list could be continued, but hopefully some of the examples my help to explain color changes in your Koi which you have observed. Unfortunately these things don't happen in isolation, making it very difficult to ascertain exactly what caused the coloration of your Koi, this can only be remedied by more people making more accurate records of the coloration of their Koi and what happens when conditions change.