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We propose a method for characterizing the image—multidimensional projection—of complex, self-organising, system. The method is general and may be used for characterisation of any structured, experimentally observable, complex self-organized systems. The method is based on calculation of information gain by which a point contributes to the total information in the image, the point information gain, PIG. We have also derived related variables, the point information gain entropy PIE and point information gain entropy density PIED. The later values are unique to a structured information and may be used for analysis of similarity by clustering, identification of states etc. We illustrate our key results using the example of living cell. We discuss practical limits of the analogy between this observable self-organising system and its possible theoretical model using an example of chaotic attractor.