This study explores the application of multi-scale fractal geometry and lacunarity analysis to improve Alzheimer’s disease detection from handwriting images. While machine learning approaches for handwriting-based Alzheimer’s detection exist, the complexity and spatial distribution characteristics captured by fractal analysis remain unexplored in this context. Our methodology examined handwriting images from 174 participants across 25 tasks, extracting fractal dimension and lacunarity features to quantify pattern complexity and spatial heterogeneity. Comparative experiments with multiple classification models demonstrated that our approach achieved a best of 75.9% accuracy and 78.4% precision using SVC. Concurrently, our approach obtained better results than Convolutional Neural Networks in task-wise classification. These interpretable geometric features complement existing methods while requiring less training time than conventional deep learning techniques. The results demonstrate that geometric analysis offers a valuable integration pathway with current methods, providing mathematically rigorous, non-invasive biomarkers that could improve early detection of Alzheimer’s in clinical settings.