Fractal dimension of diffusion-limited aggregation clusters grown on spherical surfaces

Area of Science:

• Physics
• Materials Science
• Biomedical Imaging

Background:

• Diffusion-limited aggregation (DLA) forms fractal clusters with Df=1.70 in 2D continuous systems.
• Physical systems and measurement limitations (e.g., biomedical imaging resolution) can necessitate discrete models.
• Understanding fractal properties on curved surfaces is crucial for accurate interpretation.

Purpose of the Study:

• To investigate the fractal characteristics of DLA clusters grown on spherical surfaces.
• To analyze the influence of discretization and stereographic projection on these fractal properties.
• To provide insights for interpreting biomedical images of fractal structures.

Main Methods:

• Simulating DLA cluster growth on spherical surfaces.
• Varying particle sizes to examine discretization effects (r/R ratio).
• Assessing the impact of stereographic projection on fractal dimensions.

Main Results:

• Discretization, influenced by particle size relative to sphere radius, alters fractal dimensions.
• Stereographic projection also modifies the fractal properties of DLA clusters on spheres.
• Both factors deviate from the expected continuous fractal dimension.

Conclusions:

• Discretization and projection are critical factors affecting DLA fractal dimensions on curved surfaces.
• These effects must be accounted for when analyzing fractal patterns in biomedical imaging.
• Accurate interpretation of DLA structures in curved, discrete environments requires considering these modifications.