Box-Counting Dimension Sequences of Level Sets in AI-Generated Fractals.

Lee, Minhyeok; Lee, Soyeon

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.

DISCRETE mathematics; DIGITAL image processing; COMPUTER vision; FRACTAL dimensions; SET theory

Fractal & Fractional, 2024, Vol 8, Issue 12, p730

2504-3110

Academic Journal

10.3390/fractalfract8120730