Fractals and the Cantor Set

Fractal and Cantor Set Fractal is an excellent design for infinite self-similarity. This means that no matter how small the fractal observation window is, a small part of the fractal contains all information about the whole fractal. For example, this contrasts with most features that tend to look like straight lines when examined carefully. The Cantor group is an interesting example of a fractal. The Cantor group is formed by deleting the middle third of the line segment.

Use an iterative transformation for the initial common graph (Cantor dust or von Koch curve), triangle (Sierpinski triangle), or cube (Menger sponge), fractal derived from standard geometry). The first fractal character invented in the late 19th and early 20th century belonged to this group. Fractal Expressionism is a term used to distinguish traditional visual arts including fractal elements such as self-similarity. The best example of fractal representation is Jackson Pollock 's drip mode. They were analyzed and found that their fractal dimensions are due to his technique.

Fractal and Cantor Set Fractal is an excellent design for infinite self-similarity. This means that no matter how small the fractal observation window is, a small part of the fractal contains all information about the whole fractal. For example, this contrasts with most features that tend to look like straight lines when examined carefully. The Cantor group is an interesting example of a fractal. The Cantor group is formed by deleting the middle third of the line segment.

Escape time fractal - Use formal or recursive relationships at each point in space (eg complex plane); usually quasi-self-similar type; also known as "trajectory" fractal; and Lyapunov fractal. When a point (or pixel data) passes repeatedly through a field, the two-dimensional vector field generated by one or two escaped escape time expressions also produces a fractal form. Use random rules such as random fractal - Levy flight, penetration cluster, self avoidance walking, fractal landscape, brownian motion trajectory, and brown tree (ie, dendritic fractal generated by modeling diffusion-limited agglutination or response-limiting clusters) To do.