FractalBench: Diagnosing Visual-Mathematical Reasoning Through Recursive Program Synthesis

• URL: http://arxiv.org/abs/2511.06522v1
• Date: Sun, 09 Nov 2025 20:22:42 GMT
• Title: FractalBench: Diagnosing Visual-Mathematical Reasoning Through Recursive Program Synthesis
• Abstract summary: FractalBench is a benchmark evaluating fractal program synthesis from images.<n>We evaluate four leading MLLMs -- GPT-4o, Claude 3.7 Sonnet, Gemini 2.5 Flash, and Qwen 2.5-VL -- on 12 canonical fractals.<n>Results reveal a striking disconnect: 76% generate syntactically valid code but only 4% capture mathematical structure.
• Score: 0.00954904463032233
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mathematical reasoning requires abstracting symbolic rules from visual patterns -- inferring the infinite from the finite. We investigate whether multimodal AI systems possess this capability through FractalBench, a benchmark evaluating fractal program synthesis from images. Fractals provide ideal test cases: Iterated Function Systems with only a few contraction maps generate complex self-similar patterns through simple recursive rules, requiring models to bridge visual perception with mathematical abstraction. We evaluate four leading MLLMs -- GPT-4o, Claude 3.7 Sonnet, Gemini 2.5 Flash, and Qwen 2.5-VL -- on 12 canonical fractals. Models must generate executable Python code reproducing the fractal, enabling objective evaluation. Results reveal a striking disconnect: 76% generate syntactically valid code but only 4% capture mathematical structure. Success varies systematically -- models handle geometric transformations (Koch curves: 17-21%) but fail at branching recursion (trees: <2%), revealing fundamental gaps in mathematical abstraction. FractalBench provides a contamination-resistant diagnostic for visual-mathematical reasoning and is available at https://github.com/NaiveNeuron/FractalBench

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