Fractals are complex geometric shapes that exhibit self-similarity across different scales, meaning they look similar regardless of how much they're magnified. The concept was popularized in the 20th century by mathematician Benoît B. Mandelbrot, who used the term to describe these infinitely complex patterns found both in mathematics and nature. Fractals have applications in various fields, including computer graphics, natural sciences, and telecommunications, due to their ability to accurately model naturally occurring structures. The Mandelbrot set, one of the most famous examples of fractals, showcases their infinitely intricate boundary, exemplifying the infinite complexity within fractal geometry.