A non-linear discrete transform for pattern recognition of discrete chaotic systems

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter