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Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. [1] Early Greek philosophers studied pattern, with Plato ...
Moiré pattern. A moiré pattern formed by two units of parallel lines, one unit rotated 5° clockwise relative to the other. The fine lines that make up the sky in this image create moiré patterns when shown at some resolutions for the same reason that photographs of televisions exhibit moiré patterns: the lines are not absolutely level ...
Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular ...
A level-5 approximation to a Sierpinski triangle obtained by shading the first 2 5 (32) levels of a Pascal's triangle white if the binomial coefficient is even and black otherwise If one takes Pascal's triangle with 2 n {\displaystyle 2^{n}} rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the ...
In music, consecutive fifths or parallel fifths are progressions in which the interval of a perfect fifth is followed by a different perfect fifth between the same two musical parts (or voices): for example, from C to D in one part along with G to A in a higher part. Octave displacement is irrelevant to this aspect of musical grammar; for ...
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