Through their lifespans, humans emotionally attach to those who provide physical or emotional security. Attachment phenomena include infants using their carers as secure-bases from which to explore, and return to when tired or anxious. A number of existing multi-agent system and robotic attachment simulations capture secure-base behavioural patterns where 'attached' agents or robots repeatedly recede away from and then return to their attachment targets. The infant agents in these attachment simulations can be compared with very early phototropic robots such as Grey Walter's Tortoises. So instead of phototropism, some existing attachment models demonstrate a tropic attraction to attachment targets rather than light sources. However, Attachment Theory involves research on significantly richer behavioural phenomena than just abstract patterns of exploratory and secure-base behaviour - for example research on the longitudinal stability of attachment patterns; grief responses to separations; and the use of attachment scripts in adult caregiving contexts. Therefore this talk will assess how three different elaborations of computational attachment models can help move beyond a simple 'tropic' approach. These are: learning mechanisms; the formation of richer internal representations and architectures; and the transformative effects of attachment structured environments for operating and developing within the social and physical world.