Fractal geometry lies within the mathematical branch of measure theory. Starting in the 17th century with notions of recursion, fractals have moved through increasingly rigorous mathematical treatment to the study of continuous but not differentiable functions. Fractals are a subset of Euclidean space in mathematics with a fractal dimension that strictly exceeds its topological dimension. The term fractal was used by mathematician Benoit Mandelbrot, and is based on the Latin frāctus, meaning fractured. Extending the concept of theoretical fractional dimensions to geometric patterns in nature.