Is Arethusa Pool (New Zealand) and its island's the worlds only natural fractal lake? I was there with my family in January: it was a wonderful day, and very exciting for me - mathematically speaking. Arethusa Pool (and its island) is on Mou Waho Island, which is on Lake Wanaka, which is on the South Island of New Zealand, which is in the South Pacific Ocean. Water (the South Pacific Ocean), land (South Island New Zealand), water (lake Wanaka), land (Mou Waho Island) , water (Arethusa Pool), land (islands on Arethusa Pool); water in a puddle after rain (or when I filled it), land as small as a square centimeter inside the puddle, ..... water?? Arethusa Pool, and Lake Wanaka New Zealand 2015.