We develop computational and theoretical frameworks to understand how fractal landscapes and drainage networks evolve, organize, and exhibit characteristic scaling patterns. Our research investigates fractality, scaling laws, self-organization, and optimal channel networks to identify the fundamental principles underlying realistic terrain and river-network forms. To support these studies, our laboratory introduced the Global D8 (GD8) and improved GD8 (iGD8) algorithms for flow-path extraction and developed landscape evolution models such as LEGS and DESE, which simulate dynamic Earth-surface change, including coupled topography–climate evolution. Building on these foundations, we also develop scalable computing methods for efficient, long-term, and realistic landscape simulation.