A mouse-following circle demonstrates real-time React state updates. The SVG circle tracks the cursor's `clientX` and `clientY` coordinates, while its radius randomly resets to a value between 0 and 100 on every mouse move. The app uses React's `useState` and `useCallback` hooks within a functional component, rendering through `ReactDOM.render`. Mouse events on the SVG element trigger updates to both position and radius state, showcasing React's reactive rendering with declarative SVG markup.