The Hofstadter Transcendental Triangle Variety

The Hofstadter point is a transcendental triangle center. So this gets me thinking: well, if I have three noncollinear complex numbers, that’s a triangle, right? And for three complex numbers u,v,w I can treat them as elements of \mathbb{C}

So here’s the recipe: the Hofstadter Transcendental Triangle Variety X is the set of points in (u,v,w)\in\mathbb{C}^{3} such that given some point \rho\in\mathbb{C}, the “Hofstadter mean” of those three points is \rho.

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