Role of memory in the function of biological tissues, organs and organisms remains unexplored with many unanswered questions. In this study, the emergence of associative memory in somatic (non-neural) tissues and its potential relation to tissue function was explored using a number of biologically plausible network topologies in in silico tissues with computing cells. These topologies were local cooperation; complete system-wide cooperation or inhibition; and local cooperation and short- or long-range inhibition. These were tested with and without self-feedback on two-dimensional (2D) three-dimensional (3D) cell networks, resulting in various forms of fully and partially connected networks. Further, both binary inputs with threshold processing and real-valued inputs with nonlinear processing were considered. Results revealed the emergence of diverse forms of tissue memory. In full cooperation, networks produced one fixed attractor indicating the propensity towards a stable memory pattern which in a real tissue could correspond to an invariable physiological state, such as bioelectric homeostasis. The local neighbourhood cooperation produced both a fixed and a limit cycle attractor that could be beneficial for a tissue to hold few associative memories including circadian rhythms. Most interesting results were found for the local cooperation with short- or long-range inhibition topologies that produced a cluster of fixed and limit cycle attractors offering diverse memories. Fixed attractors could correspond to inactive tissue states and active nonrhythmic functional states and limit cycles could correspond to circadian rhythms such as pumping in heart, kidney or liver in various oscillatory regimes. In all topologies, self-feedback abolished or drastically reduced the limit cycles in favour of fixed stable state. These attractor patterns were found to be largely invariant to scale (2D or 3D) and type of inputs and processing. We also explored the self-optimising ability of the ‘local cooperation with global (short- or long-range) inhibition’ 2D topologies with Hebbian learning with fixed and flexible topologies. The fixed topology learned to self-model to consolidate memory towards fewer more stable attractors. The flexible topology even formed new connections to bring the system to a single fixed state. Thus local cooperation with global inhibition topology can offer greater freedom to create diverse memory pattens that can be tempered by learning, self-feedback, and to some extent continuous processing to simplify and consolidate memory towards manageable forms.