Overview

• Researchers have identified Mainardi-Codazzi-Peterson (MCP) incompatibility as the geometric mechanism shaping the sharp cusps of rose petals, challenging traditional Gauss curvature theories.
• The study, published in *Science*, combined theoretical analysis, computational modeling, and synthetic experiments to validate MCP incompatibility as the driving force behind rose petal morphology.
• Synthetic disc experiments replicated rose petal growth patterns, demonstrating how localized stress concentrations create sharp features and influence subsequent tissue growth.
• Roses are the only known natural system to employ MCP incompatibility, highlighting their unique evolutionary adaptation compared to other plants that rely on Gaussian mechanisms.
• The findings open new possibilities for designing advanced shape-morphing materials, leveraging MCP incompatibility for precise, localized deformations in engineering applications.