Gradient Mountain Cloud App Logo

Create a clean modern app logo on a pure white background: a rounded cloud-like circular badge made from overlapping soft lobes, filled with a smooth gradient from {argument name="top color" default="violet purple"} at the upper left through {argument name="middle color" default="bright azure blue"} to {argument name="bottom color" default="cyan turquoise"} at the lower right. Inside the badge, depict a minimalist landscape icon with two white snow-covered mountain peaks: one smaller peak on the left and one larger peak centered-right, both with gentle blue shadow gradients along their lower slopes. Add a small solid white sun or moon circle in the upper-left interior. Across the bottom of the mountains, include a flowing curved white wave line separating the snowy peaks from the blue lower area, with subtle depth and glossy highlight effects. Use vector-style simplicity, rounded edges, soft gradients, no text, no border, centered composition, high-resolution app icon aesthetic.