The Fractal Geometry of the Nymphalid Groundplan: Self-Similar Configuration of Color Pattern Symmetry Systems in Butterfly Wings

SIMPLE SUMMARY: Highly diverse color patterns of butterfly wings can be explained as modifications of an archetypical color pattern of nymphalid butterflies called the nymphalid groundplan. The nymphalid groundplan contains three major symmetry systems and a discal symmetry system, but their relationships have been elusive. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species color-pattern comparisons of the hindwings in nymphalid butterflies. It was shown that all symmetry systems can be expressed as various structures, suggesting the equivalence (homology) of these systems in developmental potential. In some cases, the discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, indicating a unified supersymmetry system covering the entire wing. These results suggest that butterfly color patterns are hierarchically constructed; one system is nested within another system, which is a self-similar relationship that achieves the fractal geometry. This self-similarity is likely mediated by the serial induction of organizers during development, and a possible mechanism is proposed for symmetry breaking of the system morphology, which contributes to the diversity of butterfly wing color patterns. ABSTRACT: The nymphalid groundplan is an archetypical color pattern of nymphalid butterflies involving three major symmetry systems and a discal symmetry system, which share the basic morphogenesis unit. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species comparisons of nymphalid hindwings. Based on findings in Neope and Symbrenthia, all three major symmetry systems can be expressed as bands, spots, or eyespot-like structures, suggesting equivalence (homology) of these systems in developmental potential. The discal symmetry system can also be expressed as various structures. The discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, based mainly on findings in Agrias, indicating a unified supersymmetry system covering the entire wing. The border symmetry system can occupy the central part of the wing when the central symmetry system is compromised, as seen in Callicore. These results suggest that butterfly color patterns are hierarchically constructed in a self-similar fashion, as the fractal geometry of the nymphalid groundplan. This self-similarity is likely mediated by the serial induction of organizers, and symmetry breaking of the system morphology may be generated by the collision of opposing signals during development.