People show a tendency to devalue rewards when they are delayed in time. This so-called delay discounting often happens to an extent that seems irrational from an economical perspective. Research studying outcomes of delay discounting decisions has successfully derived descriptive models for such choice preferences. However, this outcome-based approach faces limitations in integrating the influence of contextual factors on the decision. Recently, this outcome-centred perspective on delay discounting has been complemented by a focus on the process dynamics leading to delay discounting decisions. Here, we embrace and add to this approach: We show how an attractor model can extend discounting descriptive discounting curves into the temporal dimension. From the model, we derive three predictions and study the predictions in a delay discounting experiment based on mouse tracking. We find differences in discounting depending on the order of option presentation and more direct movements to options presented first. Together with the analysis of specific temporal patterns of information integration, these results show that considering the continuous process dynamics of delay discounting decisions and harvesting them with continuous behavioural measures allow the integration of contextual factors into existing models of delay discounting, not as noise but as a signal on their own.