Fractal geometry has a large impact on nature. Since fractals can apply chaos theory, they can accurately describe random shapes created by nature.
Noises have fractal dimensions, existing between one and 0, so music and fractals are related. Some composers, like György Ligeti, are even inspired by fractals when they create music.
Fractals can describe patterns. Many scientists believe that the answer to the question of how stars were created and came to exist in the universe lies in the fractals of interstellar gases. The gases replicate the pattern that clouds make which are fractal patterns. They also describe human phenomena. Without fractals, there would be no way to describe these patterns.
Fractals can describe patterns. Many scientists believe that the answer to the question of how stars were created and came to exist in the universe lies in the fractals of interstellar gases. The gases replicate the pattern that clouds make which are fractal patterns. They also describe human phenomena. Without fractals, there would be no way to describe these patterns.
Additionally, scientists have described structures in the body to be classic Euclidean shapes. However, now some are starting to use fractal geometry to represent things like cell membranes and heartbeats since the structure repeats. Also, self-similarity has been found in DNA and chromosomes that have the same structure as trees. Therefore, they are fractals! Also, Mandelbrot wrote that the dimension of noise is in between 0 and 1, therefore noise exists in a fractional dimension.
Fractal geometry has encouraged people to study pure mathematics. All of the ideas and theories behind the fractals Mandelbrot discovered came from mathematicians studying different kinds of pure mathematics. By making their theories visual, the abstract ideas became interesting pictures which makes people more eager to study pure mathematics.
Fractal geometry also has a close relationship with physics, medicine, biology, architecture, engineering, and population dynamics. Many artists and composers have been inspired by fractals.
Fractal geometry also has a close relationship with physics, medicine, biology, architecture, engineering, and population dynamics. Many artists and composers have been inspired by fractals.
Image Compression
Pictures in computers are saved by recording the color of every pixel which takes up lots of space. Computers can try and find patterns in images and save the pattern instead of each individual pixel. Michael Barnsley and Alan Sloan found a method on how to compress images into fractals.