The dynamics of pattern formation in lateral-inhibition type neural fields with global inhibition has been extensively studied in a number of works whre it has been demonstrated that these fields are able to maintain a localized packet of neuronal activity that can for example represent the current state of an agent in a continuous space or reflect some sensory input feeding the field. Such networks most generally use excitatory recurrent collateral connections between the neurons as a function of the distance between them and global inhibition is used to ensure the uniqueness of the bubble of activity within the field. However, this full inhibitory connectivity, either implicit or explicit, is somehow problematic because the cortex, if richly connected, is not fully connected and it is the purpose of this presentation to introduce a model that perform global competition (leading to the creation of a unique bubble of activity) by only using local excitation and inhibition without the use of any supervisor or central executive. This is made possible by using a diffusion of the inhibition throughout the network. This locality yields several advantages. First, in terms of pure computational power, it is far more quicker to have a few local interactions when computing activity within the network. Second, the use of diffusion makes the model scalable to virtually any size without any change in parameters. More precisely, lateral weights do not need to be adjusted for any particular size of the network since the travelling inhibition wave ultimately reaches any neurons within a map.