Dariusz Jamroz

Multidimensional Labyrinth – Multidimensional Virtual Reality

In this paper, the author’s method which allows checking the possibility of human acquisition of skills of comprehension and intentional movement in multidimensional space was presented. The method allows to check, whether a human is able to find an exit from the n-dimensional labyrinth (for any finite n ≥ 3). It can be achieved by virtual movements in multidimensional space. The man in front of the computer screen on which he sees a picture of the interior of a multidimensional labyrinth with the goal of exiting from this labyrinth may feel like a laboratory rat which has been placed in unknown and inexplicable reality for him. In this paper we describe the computer system created on the basis of the presented theory. It allows moving in the virtual labyrinth placed in four and five-dimensional space, is also presented. This program besides research purposes may be treated as the first multidimensional game.

Application of Multidimensional Data Visualization in Creation of Pattern Recognition Systems

The paper presents the application of multidimensional data visualization to obtain the views of 5-dimensional space of features created by recognition of printed characters. On the basis of these views it was stated that the features chosen to construction of features space are sufficient to correct recognition process. This is the significant help by constructing the recognition systems because the correct selection of objects properties on the basis of which the recognition should occur is one of the hardest stages.

The Analysis of the Effectiveness of the Perspective-Based Observational Tunnels Method by the Example of the Evaluation of Possibilities to Divide the Multidimensional Space of Coal Samples

Methods of qualitative analysis of multidimensional data using visualization of this data consist in using the transformation of a multidimensional space into a two-dimensional one. In this way, multidimensional complicated data can be presented on a two-dimensional computer screen. This allows to conduct the qualitative analysis of this data in a way which is the most natural for people, through the sense of sight. The application of complex algorithms targeted to search for multidimensional data of specific properties can be replaced with such a qualitative analysis. Some qualitative characteristics are simply visible in the two-dimensional image representing this data. The new perspective-based observational tunnels method is an example of the multidimensional data visualization method. This method was used in this paper to present and analyze the real set of seven-dimensional data describing coal samples obtained from two hard coal mines. This paper presents for the first time the application of perspective-based observational tunnels method for the evaluation of possibilities to divide the multidimensional space of coal samples by their susceptibility to fluidal gasification. This was performed in order to verify whether it will be possible to indicate the possibility of such a division by applying this method. Views presenting the analyzed data, enabling to indicate the possibility to separate areas of the multidimensional space occupied by samples with different applicability for the gasification process, were obtained as a result.

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.