Scalable assembly of algorithmic DNA lattices using combined 3-input logic rules

DNA-based algorithmic self-assembly provides a versatile platform for parallel computation and nanoscale pattern generation. Logic gates constructed from DNA rule tiles enable programmable lattices capable of performing complex mathematical operations. Here, we present a combinatorial method for generating diverse algorithmic patterns using 3-input 1-output logic rules. By combining complementary rule sets (e.g., {R017, R238}) and non-complementary sets (e.g., {R019, R238}), we designed specific rule and operator tiles that reduce the number of unique tiles required while expanding the range of implementable logic functions. The resulting DNA lattices were experimentally validated using atomic force microscopy, and observed patterns closely matched theoretical predictions, demonstrating high fidelity and reliability. This approach improves scalability and efficiency compared with conventional single-rule assemblies and provides a practical route toward constructing complex computational architectures at the nanoscale, with potential applications in molecular computing, programmable nanomaterials, and DNA-based information processing.