The great density and structural complexity of pulmonary vessels and airways impose limitations on the generation of accurate reference standards, which are critical in training and in the validation of image processing methods for features such as pulmonary vessel segmentation or artery-vein (AV) separations. The design of synthetic computed tomography (CT) images of the lung could overcome these difficulties by providing a database of pseudorealistic cases in a constrained and controlled scenario where each part of the image is differentiated unequivocally. This work demonstrates a complete framework to generate computational anthropomorphic CT phantoms of the human lung automatically. Starting from biological and image-based knowledge about the topology and relationships between structures, the system is able to generate synthetic pulmonary arteries, veins, and airways using iterative growth methods that can be merged into a final simulated lung with realistic features. A dataset of 24 labeled anthropomorphic pulmonary CT phantoms were synthesized with the proposed system. Visual examination and quantitative measurements of intensity distributions, dispersion of structures and relationships between pulmonary air and blood flow systems show good correspondence between real and synthetic lungs (p > 0.05 with low Cohen's d effect size and AUC values), supporting the potentiality of the tool and the usefulness of the generated phantoms in the biomedical image processing field.