Origami and fractal solutions of differential systems

In this article we describe the fractal nature of the solutions of the Dirichlet problem associated with the definition of origami by an analytic point of view. In particular we introduce a new iterative algorithm to construct a solution of the differential problem when the boundary da- tum is not homogenous. The paper is dedicated to Michele Emmer, who few years ago invited us to give talks about this mathematical approach to origami at one of the meetings on Mathematics and Culture that he organized in Venezia.