Fractal analysis studies complex shapes and patterns using a new kind of geometry. It measures how complicated a shape is by giving it a dimension between 1 and 3. Fractals are used in geography to understand things like coastlines and city growth. But there are problems with fractal analysis, like assuming everything is self-similar and getting different results with different methods. Scientists are working on better ways to measure fractals and finding new ways to use them in studying the world.