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I know others have expirimented with toroidal coordinates in the past, but I thought the concept was intriguing enough to take another look at it. I've found some pretty interesting results, especially as you increase the power (I wonder why all mandy-style fractals look better at higher powers...). Here's the first picture, this is at power 8 with a radius 4 torus. I'll keep posting more pictures as I find new things.

By the way, the calling this a toroidal coordinate mandy is kind of misleading. It uses a power operation derived from a toroid, but it's not based on bipolar coordinates, like the true toroidal coordinates http://en.wikipedia.org/wiki/Toroidal_coordinates.

Completely agree with Johan
Some really beautiful shapes in there....would love some closeups