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I'm still puzzled by this. I mean I do understand that cross-product of two tangent vectors should be co-linear to normal in this point, but what does this have to do with this thread's attempt to define mandelbrot-like fractal using cross-product?

edit: more specifically, how does the relevance of cross-product operation to surfaces changes anything as opposed to looking at your formula like Rn+2 = f(Rn+1, Rn+0) + R0 where f just "happened" to be cross-product operation? after all, it could be (Rn+0's x, cos(Rn+1's y), Rn+1's z * Rn+0's z) or something equally stupid.