A fractal is a mathematical set that has a fractional dimension. Fractals are found in nature, where they appear as shapes that are self-similar at different scales. For example, a fern leaf is made up of many smaller leaves, each of which is a copy of the overall shape.
Fractals can be generated by iterating simple algorithms. The most famous fractal, the Mandelbrot set, is generated by repeated squaring and addition of complex numbers. Other examples include the Julia set and the Sierpinski triangle.
Fractals have several interesting properties. They are often space-filling, meaning that they can completely fill a region with no gaps or holes. They also have self-similarity, meaning that their small-scale structure is similar to their large-scale structure. And they are often scale-invariant, meaning that their appearance does not change when viewed at different scales.
Fractals have applications in many fields, including medicine (where they are used to model tumor growth), engineering (where they are used to design more efficient buildings), and computer graphics (where they are used to generate realistic images).