Although conventional computer technology made a huge leap forward in the past decade, a vast number of computational problems remain inaccessible due to their inherently complex nature. One solution to deal with this computational complexity is to highly parallelize computations and to explore new technologies beyond semiconductor computers. Here, we report on initial results leading to a device employing a biological computation approach called network-based biocomputation (NBC). So far, the manufacturing process relies on conventional Electron Beam Lithography (EBL). However we show first promising results expanding EBL patterning to the third dimension by employing Two-Photon Polymerization (2PP). The nanofabricated structures rely on a combination of physical and chemical guiding of the microtubules through channels. Microtubules travelling through the network make their way through a number of different junctions. Here it is imperative that they do not take wrong turns. In order to decrease the usage of erroneous paths in the network a transition from planar 2-dimensional (mesh structure) networks to a design in which the crossing points of the mesh extend into the 3rd dimension is made. EBL is used to fabricate the 2D network structure whereas for the 3D-junctions 2PP is used. The good adaptation of the individual technologies allows for the possibility of a future combination of the two complementary approaches.