complex solutions of diophantine polynomials and trees

Chaitin has implemented an exponential polynomial that more or less is a lisp implementation, and Yuri Matiyasevich implemented one in the seventies that was used in his proof to answer Hilbert’s 10th problem in the negative.

In Baez’s This Week’s Finds, week 202, an isomorphism between trees and seven tuples of trees is noted.

This makes me wonder: what could we do with complex solutions of Chaitin’s and Matiyasevich’s polynomials?

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