GENERATION OF COMPOSITIONAL GRIDS BASED ON FRACTAL STRUCTURES AND RECURRENT MODELS

Abstract

The article addresses the scientific and practical task of formalizing and automating the construction of complex compositional structures for digital design. The object of study is the processes of generating compositional grids, and the subject is mathematical models based on fractal structures and recurrent algorithms. The purpose of the work is the development and software implementation of methods for automated generation of nine types of grids (including fractal, stochastic, and iterative) to increase the variability and substantiation of design solutions. The study applies methods of mathematical modeling, fractal theory, and algorithmic design. The scientific novelty lies in the integrated approach to parameterizing fractal and recurrent structures (Sierpinski carpet, binary partition, golden ratio, etc.) for compositional layout needs, as well as in defining formal criteria of their applicability (density, symmetry, scalability). The analysis shows that the use of iterative models, such as Quadtree and Binary Split, allows for achieving an optimal balance between visual complexity and functional logic of the interface. The practical significance is confirmed by the development of a specialized plugin for the Figma environment (TypeScript, Figma Plugin API), which automates the creation of adaptive layouts and significantly reduces the time required for preparing initial compositional solutions in professional UI/UX design practice.

The research emphasizes the relevance of bridging theoretical achievements of mathematical modeling with practical design tools. The proposed algorithms provide a systematic approach to constructing compositional structures that go beyond intuitive or standard modular solutions. The study introduces formalized criteria for evaluating the suitability of models, which create a basis for a justified choice of an optimal grid depending on the functional purpose of the interface and content dynamics. The conducted analysis demonstrated the advantages of fractal structures in creating hierarchical systems that maintain integrity during scaling. The plugin implementation illustrates the feasibility of integrating complex mathematical structures into everyday workflows, ensuring both aesthetic harmony and functional flexibility. The results open perspectives for further development of generative design methods, expansion of the library of grid generators, optimization of algorithms for big data, and integration with intelligent systems supporting creative processes in modern digital environments.

Keywords: compositional grids, fractal structures, recurrence algorithms, generative design, automated design, Figma API, stochastic partitioning, quadtree, golden ratio, Sierpinski carpet, UI/UX design.