Matsukawabake
The Matsukawabake is an oddity, in that the distribution of black and white areas changes according to the seasons and the temperature of the water in which it is kept. However, this does not amount to a complete reversal of pattern. The Koi can turn completely black or completely white under some circumstances, but can display interesting shadowy sumi in the transition period.
It's hard to believe, but these two photos are of the same Koi! Kumonryu are known to change their coloring with the seasons. They're like having two Koi in one.