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The structures of minerals provide good examples of regularly repeating three-dimensional arrays. Despite the hundreds of thousands of known minerals, there are rather few possible types of arrangement of atoms in a crystal , defined by crystal structure , crystal system , and point group ; for example, there are exactly 14 Bravais lattices for ...
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.
This layer-by-layer growth is two-dimensional, indicating that complete films form prior to growth of subsequent layers. [2] [3] Stranski–Krastanov growth is an intermediary process characterized by both 2D layer and 3D island growth. Transition from the layer-by-layer to island-based growth occurs at a critical layer thickness which is ...
The model, named after Murray Eden, was first described in 1961 [2] as a way of studying biological growth, and was simulated on a computer for clusters up to about 32,000 cells. By the mid-1980s, clusters with a billion cells had been grown, and a slight anisotropy had been observed.
Fractal Art is a subclass of two-dimensional visual art, and is in many respects similar to photography—another art form that was greeted by skepticism upon its arrival. Fractal images typically are manifested as prints, bringing fractal artists into the company of painters, photographers, and printmakers. Fractals exist natively as ...
A two-dimensional, or plane, spiral may be easily described using polar coordinates, where the radius is a monotonic continuous function of angle : r = r ( φ ) . {\displaystyle r=r(\varphi )\;.} The circle would be regarded as a degenerate case (the function not being strictly monotonic, but rather constant ).
Chromostereopsis is a visual illusion whereby the impression of depth is conveyed in two-dimensional color images, usually of red–blue or red–green colors, but can also be perceived with red–grey or blue–grey images. [1] [2] Such illusions have been reported for over a century and have generally been attributed to some form of chromatic ...
This is the most three-dimensional of the lichen growth forms, and the most sensitive to air pollution. [41] The term "fruticose" is derived from the Latin word fruticosus , meaning "shrubby" or "similar to a shrub" (from frutex , meaning "shrub").