2010/09/15 by Gabriel Landini · 77 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Cell Image Analysis Techniques #Computer science #Force Microscopy Techniques and Applications #Fractal #Fractal analysis #Fractal dimension #Geometry #Mandelbrot set #Mathematical analysis #Mathematics #Randomness #Self-similarity #Theoretical and Computational Physics
paper · doi:10.1111/j.1365-2818.2010.03454.x
published in Journal of Microscopy 241(1), 1-8 (Wiley)
openalex publication_date 2010/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Fractal geometry, developed by B. Mandelbrot, has provided new key concepts necessary to the understanding and quantification of some aspects of pattern and shape randomness, irregularity, complexity and self-similarity. In the field of microscopy, fractals have profound implications in relation to the effects of magnification and scaling on morphology and to the methodological approaches necessary to measure self-similar structures. In this article are reviewed the fundamental concepts on which fractal geometry is based, their relevance to the microscopy field as well as a number of technical details that can help improving the robustness of morphological analyses when applied to microscopy problems.