We have developed a novel extension of the NEAT neuroevolution method, termed NEATfields, to solve problems with large input and output spaces. NEATfields networks are layered into two-dimensional fields of identical or similar subnetworks with an arbitrary topology. The subnetworks are evolved with genetic operations similar to those used in the NEAT neuroevolution method. We show that information processing within the neural fields can be organized by providing suitable building blocks to evolution. NEATfields can solve a number of visual discrimination tasks and a newly introduced multiple pole balancing task.