Математичне моделювання ландшафтів методом процедурної генерації на основі градієнтного шуму

Abstract

This work is devoted to the mathematical modeling of continuous topographical surfaces using procedural generation systems based on gradient noise algorithms. The fundamental mathematical models of 2D noise generation and Fractional Brownian Motion were analyzed. A comparative calculation of the computational efficiency of SIMD-vectorized synthesis relative to scalar generation methods is carried out. It has been found that while gradient noise systems provide coherent topology, memory access patterns and architectural overheads crucially impact the scaling limits of procedural algorithms