Fractals are geometric shapes or patterns that exhibit self-similarity at different scales. This means that the same pattern or shape is repeated at smaller and smaller scales within the overall structure. Fractals can be found in many natural phenomena, including trees, clouds, coastlines, and ferns, as well as in man-made objects such as antennas and computer-generated images.
The study of fractals is known as fractal geometry, and it has important applications in many fields, including mathematics, physics, computer science, biology, and art. Fractal geometry has been used to model and analyze complex systems and phenomena, such as the behavior of stock prices, the growth of tumors, the structure of galaxies, and the distribution of earthquakes.
One of the most famous fractals is the Mandelbrot set, which is a complex mathematical object discovered by mathematician Benoit Mandelbrot in the 1970s. The Mandelbrot set is generated by a simple mathematical formula, but it exhibits incredibly intricate and beautiful patterns that repeat at different scales. The study of the Mandelbrot set and other fractals has led to new insights and discoveries in mathematics and other fields, and it has also inspired artists and designers to create new forms of art and visual representation.
