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The brain functions as a spatio-temporal information processing machine and deals extremely well with spatio-temporal data. Spatio- and spectro-temporal data (SSTD) are the most common data collected to measure brain signals and brain activities, along with the recently obtained gene and protein data. Yet, there are no computational models to integrate all these different types of data into a single model to help understand brain processes and for a better brain signal pattern recognition. The EU FP7 Marie Curie IIF EvoSpike project develops methods and tools for spatio and spectro temporal pattern recognition. This paper proposes a new evolving spiking model called NeuCube as part of the EvoSpike project, especially for modeling brain data. The NeuCube is 3D evolving Neurogenetic Brain Cube of spiking neurons that is an approximate map of structural and functional areas of interest of an animal or human brain. Optionally, gene information is included in the NeuCube in the form of gene regulatory networks that relate to spiking neuronal parameters of interest. Different types of brain SSTD can be used to train a NeuCube, including: EEG, fMRI, video-, image- and sound data, complex multimodal data. Potential applications are: EEG -, fMRI-, and multimodal brain data modeling and pattern recognition; Brain-Computer Interfaces; cognitive and emotional robots; neuro-prosthetics and neuro-rehabilitation; modeling brain diseases. Analysis of the internal structure of the model can trigger new hypotheses about spatio-temporal pathways in the brain.