The synthetic generation of static handwritten signatures based on motor equivalence theory has been recently proposed for biometric applications. Motor equivalence divides the human handwriting action into an effector dependent cognitive level and an effector independent motor level. The first level has been suggested by others as an engram, generated through a spatial grid, and the second has been emulated with kinematic filters. Our paper proposes a development of this methodology in which we generate dynamic information and provide a unified comprehensive synthesizer for both static and dynamic signature synthesis. The dynamics are calculated by lognormal sampling of the 8-connected continuous signature trajectory, which includes, as a novelty, the pen-ups. The forgery generation imitates a signature by extracting the most perceptually relevant points of the given genuine signature and interpolating them. The capacity to synthesize both static and dynamic signatures using a unique model is evaluated according to its ability to adapt to the static and dynamic signature inter- and intra-personal variability. Our highly promising results suggest the possibility of using the synthesizer in different areas beyond the generation of unlimited databases for biometric training.