We present a discrete numerical computational approach for modelling the CO(2)eq emissions when transitioning from existing legacy electricity production technologies based on fossil fuels, to new and potentially sustainable alternatives based on renewable energy. This approach addresses the dynamic nature of the transition, where the degree of transition has an ongoing, beneficial and compounding effect on future technological deployments. In other words, as the energy system evolves, renewable energy technologies are made increasingly with renewable energy, thus becoming renewable energy 'breeders'. We apply this routine to tour previously published scenarios for the transition of the Australian electricity sector, which at present.accounts for about one-third of the country's annual CO(2)eq emissions. We find that three of the four scenarios fail to satisfy the electricity sector's proportion of Australia's share of the 2.0 degrees C/66% IPCC carbon budget, and none of them achieves the 1.5 degrees C budget. Only the High Carbon Price scenario could be deemed to have made any meaningful impact. An urgent, rapid transition to 100% renewable energy must be made in the whole energy sector, not just electricity, if the 1.5 degrees C budget is to be satisfied. (C) 2017 Elsevier Ltd. All rights reserved.