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For this he defines statistically self-similar figures and says that these are encountered in nature. The paper is important because it is a "turning point" in Mandelbrot's early thinking on fractals. [14] It is an example of the linking of mathematical objects with natural forms that was a theme of much of his later work.
Spatial ecology studies the ultimate distributional or spatial unit occupied by a species.In a particular habitat shared by several species, each of the species is usually confined to its own microhabitat or spatial niche because two species in the same general territory cannot usually occupy the same ecological niche for any significant length of time.
A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. [1]
The nitrogen cycle is the transformation of nitrogen and nitrogen-containing compounds in nature. It is a cycle which includes gaseous components. The water cycle, is the continuous movement of water on, above, and below the surface of the Earth. Water can change states among liquid, vapour, and ice at various places in the water cycle.
The recursive nature of some patterns is obvious in certain examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. Similarly, random fractals have been used to describe/create many highly irregular real-world objects, such as coastlines and mountains.
For example, the lifespan of a feature could be considered as the temporal extent of its existence. The location of a city can change over time as annexations expand its extent. The resident population of a country changes frequently due to immigration, emigration, birth, and death.
For example, Albany, New York is roughly 140 miles north of New York City. Every site on Earth has a unique absolute location, which can be identified with a reference grid (such as latitude and longitude). Maps and globes can be used to find location and can also be used to convey other types of geographical information.
For example, we can represent individuals' incomes or years of education within a coordinate system where the location of each individual can be specified with respect to both dimensions. The distance between individuals within this space is a quantitative measure of their differences with respect to income and education.