In this paper we propose model maps to derive and represent the intrinsic functional geometry of a brain from functional magnetic resonance imaging (fMRI) data for a specific task. Model maps represent the coherence of behavior of individual fMRI-measurements for a set of observations, or a time sequence. The maps establish a relation between individual positions in the brain by encoding the blood oxygen level dependent (BOLD) signal over a time period in a Markov chain. They represent this relation by mapping spatial positions to a new metric space, the model map. In this map the Euclidean distance between two points relates to the joint modeling behavior of their signals and thus the co-dependencies of the corresponding signals. The map reflects the functional as opposed to the anatomical geometry of the brain. It provides a quantitative tool to explore and study global and local patterns of resource allocation in the brain. To demonstrate the merit of this representation, we report quantitative experimental results on 29 fMRI time sequences, each with sub-sequences corresponding to 4 different conditions for two groups of individuals. We demonstrate that drug abusers exhibit lower differentiation in brain interactivity between baseline and reward related tasks, which could not be quantified until now.