Is finding the percolation threshold of an arbitrary continuum system P or NP complex?

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By arbitrary I mean an infinite 2D system of e.g. 3 different sizes of rectangle like in figure 5 of https://doi.org/10.1103/PhysRevE.88.012101

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Introduire la question de percolation Z^2: est-ce qu'il peut y avoir (avec probabilite>0) des chemins ouvert partant de 0 allant arbitrairement loin?