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Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT --the satisfiability problem of quantified boolean formulae-- can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article, we propose an approach for constructing a particular generic machine for the same task. This machine deploys the Map/Reduce paradigm over a discrete fractal structure. Moreover our approach is modular : the machine is constructed by combining modules. In this manner, we can easily create generic machines for solving satifiability variants, such as SAT, #SAT, MAX-SAT.