{'fraction_non_alphanumeric': 0.024012393493415957, 'fraction_numerical': 0.008520526723470178, 'mean_word_length': 5.065727699530516, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Topological Approach to the Object Evolution

The early chapters have shown some of the problems that the new idea of self-formation faces. It enables to clarify the objects evolution with complexity increasing and its mechanism. Approximation by differential equations excluding causes of evolution and requiring a priori external definition of the initial and boundary conditions, was changed by numerical simulation similar to the cellular automata idea; however, more complex because the set in this case is not permanent but the function of the object surface is. Thus, it is defined only for the next step of time, and it can be changed for any next step following the object surface evolution. To satisfy all these conditions a topological apparatus was chosen [101,126,118]. Any theory describing the distinct phenomenon of the material world is constructed on its approximation adequate to this world within the limits of the phenomenon. Consequently, when creating the self-formation theory, we have to use the concepts of the object, medium, structure, interaction, formation, etc. When the chosen finite space as a part of Euclidean space covered by a distinct surface is determined, we can call this structure the topological system comprising an object and a medium (Fig. 4.1)