Year: 2024
Type: article
Abstract: We introduce a mathematical framework to characterize the hierarchical complexity of AI-generated fractals within the finite resolution constraints of digital images. Our method analyzes images produced by text-to-image models at multiple intensity thresholds, employing a discrete level set approach and box-counting dimension estimates. By conducting experiments on fractals created with the FLUX model at a resolution of 128×128, we identify a fully monotonic behavior in the dimension sequences for various box sizes, with inter-scale correlations surpassing 0.95. Pattern-specific dimensional gradients quantify how fractal complexity changes with threshold levels, offering insights into how text-to-image models encode fractal-like geometry through dimensional sequences.
Source: Fractal and Fractional
Authors: Minhyeok Lee, Soyeon Lee
Institution: Chung-Ang University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,069
Award: G3074897916
OpenAlex ID: W4405330735