I'm not completely sure if I already posted the story of how the koi turns into a dragon here on the blog. So I'll keep it short, I don't want to be repeating myself, now do I?
The koi fish in Japanese folklore represents the overcoming of obstacles, because the koi fish travels up the yellow river and when it successfully climbs the waterfall at the end of the river it transforms into the dragon.
Thus representing that if one is able to overcome obstacles/challenges they will be greater for it.
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