Create a sophisticated typographic logo design for 'FROYD', focusing on a unique and memorable treatment of the letter 'F'. The 'F' should be a distinctive design element with a modern, abstract twist that subtly hints at psychology/therapy - perhaps with flowing, continuous lines or a clever negative space design. Use a gradient color scheme of deep purple to indigo blue (#6C5DD3 to #4839A3). The typography should be clean, modern, and slightly bold with perfect letter spacing. The overall style should be minimal yet impactful, suitable for both dark and light backgrounds, with a transparent background (PNG format). Add subtle depth with minimal shadows or lighting effects to give it a contemporary tech feel. The design should work well at both small and large sizes, maintaining its clarity and sophistication, Sophisticated typographic logo for FROYD. Unique treatment of the letter F. Modern abstract twist hinting at psychology. Flowing lines or clever negative space design. Gradient colors from deep purple to indigo blue. Clean, modern typography. Slightly bold with perfect letter spacing. Minimal yet impactful style. Suitable for dark and light backgrounds. Transparent background. Subtle depth with minimal shadows. Works in various sizes
