The unique cumulative nature of human culture has often been explained by high-fidelity copying mechanisms found only in human social learning. However, transmission chain experiments in human and non-human primates suggest that cumulative cultural evolution (CCE) might not be dependent on high-fidelity copying after all. In this study we test whether CCE is possible even with a non-copying task. We performed transmission chain experiments in Guinea baboons and children where individuals observed and reproduced visual patterns on touch screen devices. In order to be rewarded, participants had to avoid touching squares that were touched by a previous participant. In other words, they were regarded for innovation rather than copying. Results nevertheless exhibited two fundamental properties of CCE: an increase over generations in task performance and the emergence of systematic structure. However, CCE arose from different mechanisms across species: children, unlike baboons, converged in behaviour over generations by copying specific patterns in a different location, thus introducing alternative copying mechanisms into the non-copying task. We conclude that CCE can result from non-copying tasks and that there is a broad spectrum of possible mechanisms that will lead to CCE aside from high-fidelity transmission.