The generation of fractal in mathematical sense is based on iterative equation, that is, recursive feedback system. There are several types of fractals, which can be defined according to exact self-similarity, semi-self-similarity and statistical self-similarity. Although fractals are a mathematical structure, they can also be found in nature, which makes them classified as works of art. Fractal has applications in medicine, soil mechanics, seismology and technical analysis.
Simply put, fractal is the study of infinitely complex geometry with self-similar structure.
It is an inherent mathematical order under the complex surface of nature.
Fractal geometry is a kind of geometry that takes irregular geometry as the research object. Compared with traditional geometry, the research object is integer dimensions, such as zero-dimensional points, one-dimensional lines, two-dimensional surfaces, three-dimensional solids and even four-dimensional time and space. The research objects of fractal geometry are non-negative real dimensions, such as 0.63, 1.58, 2.72 and log2/log3 (see Cantor set). Because its research object exists in nature, fractal geometry is also called "geometry of nature".
The generation of fractal in mathematical sense is based on iterative equation, that is, recursive feedback system. There are several types of fractals, which can be defined according to exact self-similarity, semi-self-similarity and statistical self-similarity. Although fractals are a mathematical structure, they can also be found in nature, which makes them classified as works of art. Fractal has applications in medicine, soil mechanics, seismology and technical analysis.
origin
Fractal geometry
Fractal geometry
Many things in the objective nature have a self-similar "hierarchical" structure, and in an ideal situation, they even have infinite hierarchies. Appropriately enlarge or reduce the geometric size of things, and the overall structure remains unchanged. Behind many complex physical phenomena is fractal geometry that reflects this hierarchical structure.
All objective things have their own characteristic scales, which should be measured by appropriate scales. Measuring the Great Wall of Wan Li with a ruler is too short and measuring Escherichia coli is too long. Other things have no characteristic scale, so we must consider multiple scales (or scales) from small to large at the same time. This is the problem of "scale-free".
Turbulence is a common phenomenon in nature, from the light smoke in a quiet room to the vortex in Jupiter's atmosphere, it is a very chaotic fluid movement. The energy of fluid macro-motion is transformed into thermal motion on molecular scale through many eddies on large, medium, small and micro scales, and involves a large number of motion States on different scales. To describe the turbulence phenomenon, we need to rely on the "scale-free" of the fluid, and the high vortex region in the turbulence needs fractal geometry.