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The primary brain image segmentation goal is to partition a given brain image into different regions representing anatomical structures. Magnetic resonance image (MRI) segmentation is especially interesting because the accurate representation of white matter, grey matter and cerebrospinal fluid provides a way to identify many brain disorders, such as dementia, schizophrenia or Alzheimer's disease (AD). This paper presents a fully unsupervised method for MRI segmentation based on Self-Organising Maps (SOMs) and Genetic Algorithms (GAs). In particular, the proposed method is based on five stages consisting of image acquisition, feature extraction, feature selection using evolutionary computation, voxel classification using SOM, and sharp map clustering. Moreover, a novel SOM clustering mechanism is presented that defines cluster borders by considering the output space and the relationship with the input space. This clustering mechanism accommodates spatial relationships using an entropy-gradient (EG) function calculation to group the units on the output space (SOM). The complete procedure does not use any a priori knowledge regarding voxel class assignment, but reveals a fully unsupervised, automated method for MRI segmentation to directly identify different tissue classes. Our algorithm was tested using images from the Internet Brain Image Repository (IBSR), outperforming the CGMM method in WM and CSF delineation, and was found to be the most effective among other techniques. Furthermore, this method provided excellent results using high-resolution MR images provided by the Nuclear Medicine Service of the ''Virgen de las Nieves'' Hospital (Granada, Spain).