Demonstration of Big Bang-like patterns through logic-implemented DNA algorithmic assembly

A DNA algorithm-based logic gate provides an efficient platform for generating various patterns through self-assembly. Self-assembly algorithms using M-input N-output logic gates are easily implemented in DNA tiles. The patterns generated by a 3-input 1-output logic gate show interesting features, such as demonstrations of mathematical functions, physical phenomena observed in nature, and logic operators. We notice that among the 3-input 1-output logic rules, the algorithmic lattices generated by R30 show interesting Big Bang-like patterns. A pattern generated by R30 and specific initial values shows expanding characteristics during the growth of lattices that resemble the Big Bang expansion of the universe. In this study, we demonstrate Big Bang-like patterns using simulations generated by R30 and analyze pattern sizes as a function of growth step number. We discuss pattern sizes and pattern-size-expansion-speeds, both of which are heavily influenced by perturbed initial values. We examine eight different perturbed initial values that induce Big Bang-like patterns with the generation of multiple pattern sizes during the growth of patterns. In addition, we fabricate patterns using DNA algorithmic self-assembly generated by the R30 logic rule with a 3-input 1-output logic operation. The generated algorithmic patterns are visualized by an atomic force microscope. Our method allows the generation and analysis of naturally occurring patterns, such as those found on lizard skin and Zelkova serrata lenticel patterns.