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The capacity to represent recursive hierarchical embedding (RHE) is considered a hallmark of human cognition. Yet, it remains debated whether non-linguistic recursion depends on language-specific, domain-general, or independent visuospatial mechanisms. In two experiments, we tested this question using a dual-task paradigm. Participants performed either a visual recursion task (REC) or a matched visual iteration task (ITE) while concurrently engaging in lexical retrieval (LEX), serial arithmetic (MATH), visual delayed match-to-sample (VIS), or no interference (NONE). Both LEX and MATH-tasks that require serial, symbolic, generative processing-reliably reduced accuracy in REC and ITE, with interference being stronger for ITE. Drift diffusion modeling confirmed that LEX and MATH slowed evidence accumulation and reduced decision thresholds, indicating less efficient and more impulsive responding. Interestingly, while LEX and MATH lengthened response times in ITE, they shortened them in REC, suggesting compensatory processing strategies. By contrast, VIS did not impair accuracy; instead, it increased drift and boundary separation, consistent with more cautious evidence accumulation. Cognitive covariates further revealed that verbal working memory predicted REC more strongly than ITE under baseline conditions; however, this advantage did not account for the greater interference observed in ITE. Taken together, these findings suggest that visual hierarchical processing involves serial symbolic resources, but recursion is more resilient than iteration, possibly due to the availability of parallel or configural strategies. This supports a hybrid architecture in which linguistic-like symbolic operations contribute to building visual hierarchies, but alternative mechanisms can buffer recursion when these resources are taxed.