The segmentation and classification of blood vessels in fundus images is of great importance in the detection of cardiovascular diseases, where their morphology can be a useful indicator. While the automatic segmentation of blood vessels has been solved successfully, the automatic classification between arteries and veins (A/V) remains an unanswered question. There are some proposals that use artificial intelligence such as neural networks or methods based on deep learning, with very promising results. In this work we propose a novel method based on cellular automata with a neural network as a transition function, to classify artery and vein at the pixel level given the segmentation mask. The preliminary evaluation of this new method was carried out in a local database of 36 images, yielding an accuracy of 0.9650 and 0.9679 for arteries and veins classification, and a Dice similarity index above 0.7891 in the test set. The presented classification work paves the way for automated analysis of arteries and veins, which is specifically valuable in large data sets like our population-based sample.