Box-Counting Dimension Sequences of Level Sets in AI-Generated Fractals
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/12/730 |
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| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>128</mn><mo>×</mo><mn>128</mn></mrow></semantics></math></inline-formula>, 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. |
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| ISSN: | 2504-3110 |