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Fraktals, also known as fractals, are geometric shapes that exhibit self-similarity at various scales. This means that the pattern or shape of the fractal is repeated at smaller and smaller scales, often infinitely. The term "fractal" was coined by mathematician Benoît Mandelbrot in the 1970s.

Fractals are found in nature and can be generated using mathematical equations. They are characterized by their fractional Hausdorff dimension, which is a measure of their complexity. This dimension is not an integer, unlike the dimensions of Euclidean geometry, which are 1, 2, or 3.

Some well-known examples of fractals include the Mandelbrot set, the Koch snowflake, and the Sierpinski triangle. These shapes are often used in art, computer graphics, and scientific research. In art, fractals are used to create intricate and detailed images. In computer graphics, fractals are used to generate realistic landscapes and textures. In scientific research, fractals are used to model complex systems, such as the structure of the human lung or the distribution of galaxies in the universe.

Despite their complexity, fractals are relatively simple to generate using mathematical equations. This makes them a useful tool for studying complex systems and for creating visually appealing images. However, the study of fractals is still an active area of research, with many open questions and challenges remaining.