Act as a professional logo designer with 10+ years of experience in abstract and minimalist branding. Create a visually striking logo for [DANCE COMPANY NAME], an avant-garde dance troupe specializing in [CONTEMPORARY/BREAKING/BALLET] styles. The logo should embody [ENERGY/FLUIDITY/PRECISION] through abstract shapes, negative space, or dynamic lines. Use a [MONOCHROMATIC/DUOTONE/VIBRANT] color palette and ensure scalability for both digital and print media. Avoid literal depictions of dancers—focus on evoking movement and artistry through geometry. The final design should feel modern, timeless, and distinct within the performing arts industry. Include 3 stylistic variations exploring different abstract interpretations of dance motion.