Fractals

Fractals are geometric shapes or patterns that are made up of smaller copies of themselves, known as self-similarity. They are infinitely complex and can be zoomed into indefinitely, with each zoom revealing a smaller version of the same pattern. Fractals are found in many natural objects and phenomena, such as snowflakes, mountains, and coastlines, and they are often used to model complex systems in science and mathematics.

Fractals were first discovered by French mathematician Gaston Julia in the early 20th century. Julia was interested in understanding the behavior of certain types of functions, and he found that some of these functions produced shapes that were infinitely complex and self-similar. He called these shapes "fractals," from the Latin word "fractus," meaning broken or fractured.

Julia's work on fractals was later expanded upon by Polish mathematician Benoit Mandelbrot, who developed the concept of fractal dimension. This allowed for the measurement and quantification of the complexity of fractal shapes.

Fractals have many interesting properties and have been used to model a wide range of phenomena, including stock market trends, the growth of plants, and even the structure of the universe. They are also often used in computer graphics and art, as they can produce visually stunning and complex patterns.