Abstract: An improved method is provided for solving waveform description, matching and comparison problems using attractor-based processes to extract identity tokens that indicate sequence and subsequence symbol content and order of the waveform or waveform segments. The waveform is described with a suitable alphabet to extract the ontology of the waveform, and syntactical rules are applied to direct pattern extraction using the alphabet. The patterns are extracted in a hierarchical, embedded manner according the global or local maximia and minimia so that the resulting statements are compatible with analysis in catastrophe theory. The attractor processes map the resulting waveform sequence from its original sequence representation space (OSRS) into a hierarchical multidimensional attractor space (HMAS). The HMAS can be configured to represent equivalent symbol distributions within two symbol sequences or perform exact symbol sequence matching.

Abstract: An improved method is provided for solving waveform description, matching and comparison problems using attractor-based processes to extract identity tokens that indicate sequence and subsequence symbol content and order of the waveform or waveform segments. The waveform is described with a suitable alphabet to extract the ontology of the waveform, and syntactical rules are applied to direct pattern extraction using the alphabet. The patterns are extracted in a hierarchical, embedded manner according the global or local maximia and minimia so that the resulting statements are compatible with analysis in catastrophe theory. The attractor processes map the resulting waveform sequence from its original sequence representation space (OSRS) into a hierarchical multidimensional attractor space (HMAS). The HMAS can be configured to represent equivalent symbol distributions within two symbol sequences or perform exact symbol sequence matching.