The objective of this work is to design a molecular generator capable of exploring known as well as unfamiliar areas of the chemical space. Our method must be flexible to adapt to very different problems. Therefore, it has to be able to work with or without the influence of prior data and knowledge. Moreover, regardless of the success, it should be as interpretable as possible to allow for diagnosis and improvement. We propose here a new open source generation method using an evolutionary algorithm to sequentially build molecular graphs. It is independent of starting data and can generate totally unseen compounds. To be able to search a large part of the chemical space, we define an original set of 7 generic mutations close to the atomic level. Our method achieves excellent performances and even records on the QED, penalised logP, SAscore, CLscore as well as the set of goal-directed functions defined in GuacaMol. To demonstrate its flexibility, we tackle a very different objective issued from the organic molecular materials domain. We show that EvoMol can generate sets of optimised molecules having high energy HOMO or low energy LUMO, starting only from methane. We can also set constraints on a synthesizability score and structural features. Finally, the interpretability of EvoMol allows for the visualisation of its exploration process as a chemically relevant tree.