The article is devoted to the construction of the equation of fractal complex structures based on the theories of Rvachev R-functions (RFM), the application of the recursion procedure. Using the equation of objects elementary geometries and constructive means of the method of R-functions R0: R-conjunctions, R-disjunctions and R-reflections, various fractal equations are constructed. Based on these equations, specifying the number of iteration and the angle of inclination various pre-fractals are generated

This article examines a system for creating a national virtual university based on 3D technologies in metaspace. It describes methods for developing 3D models of exterior and interior objects, visualization algorithms using R-functions (RFM), a functional IDEF1x model of a graphical database, and the architecture of the vacademia.uz software tool. Practical testing confirmed a fourfold increase in the speed of 3D object display and a 10–13% increase in productivity. This article presents a national virtual university system based on 3D technologies in metaspace, implemented as the vacademia.uz software tool. A functional IDEF1x model of the graphical database, visualization algorithms using the R-function method (RFM), a 3D model converter to the BMF format, and a client-server architecture on the vAcademia platform have been developed. The results of this study open up a number of promising areas for further research, some of which are directly related to the integration of student engagement monitoring systems into the virtual educational environment.

Сomputational Experience Optimization of Colors in Complex Fractal Images in Carpet Design Using the Simplex Method

We present a reproducible, web-scale pipeline for building a Kazakh-language corpus from the national e-government portal. The system treats the website as a directed graph and performs breadth-first traversal to preserve section hierarchy. Static acquisition relies on robust HTTP requests and HTML parsing; for pages with dynamic widgets, we selectively enable a headless layer to render the final DOM prior to extraction. We define a minimal JSON schema aligned with downstream NLP needs (URL, category, titles, cleaned descriptions) and implement normalization (Unicode NFC/NFKC, transliteration repair for Kazakh, boilerplate removal) and fragment-level deduplication. To strengthen the scientific contribution, we formalize the crawling–extraction process as an optimization under resource constraints and propose field-level quality metrics (precision, recall, F1), coverage of categories, and completeness gains attributable to headless rendering. Our experimental protocol compares static parsing against a hybrid static+headless setup on multiple portal categories, reports field-wise effectiveness with confidence intervals, and analyzes dominant error sources (DOM drift, client-side rendering, code-switching). Ablation studies quantify the impact of normalization and duplication. We also outline ethical access (robots.txt compliance, throttling, conditional requests) and provide artifacts to ensure reproducibility (versioned scripts, schema validators, logging). We release open-source scripts, detailed runbooks, and a small, labeled benchmark to facilitate fair comparisons and independent replication across institutions. The resulting corpus targets low-resource Kazakh NLP and e-government analytics, supporting tasks such as classification, terminology normalization, named-entity recognition, and LLM adaptation. Overall, the proposed pipeline demonstrates that selective headless rendering combined with rigorous normalization is a practical and effective strategy for high-quality data acquisition in dynamically rendered public portals.