Application of Perspective-Based Observational Tunnels Method to Visualization of Multidimensional Fractals

Methods of multidimensional data visualization are frequently applied in the qualitative analysis allowing to state some properties of this data. They are based only on using the transformation of the multidimensional space into a two-dimensional one which represents the screen in a way ensuring not to lose important properties of the data. Thanks to this it is possible to observe some searched data properties in the most natural way for human beings–through the sense of sight. In this way, the whole analysis is conducted excluding applications of complex algorithms serving to get information about these properties. The example of a multidimensional data visualization method is a relatively new method of perspective-based observational tunnels. It was proved earlier that this method is efficient in the analysis of real data located in a multidimensional space of features obtained by characters recognition. Its efficiency was also shown by the analysis of multidimensional real data describing coal samples. In this paper, another aspect of using this method was shown–to visualize artificially generated five-dimensional fractals located in a five-dimensional space. The purpose of such a visualization can be to obtain views of such multidimensional objects as well as to adapt and teach our mind to percept, recognize and perhaps understand objects of a higher number of dimensions than 3. Our understanding of such multidimensional data could significantly influence the way of perceiving complex multidimensional relations in data and the surrounding world. The examples of obtained views of five-dimensional fractals were shown. Such a fractal looks like a completely different object from different perspectives. Also, views of the same fractal obtained using the PCA, MDS and autoassociative neural networks methods are presented for comparison.