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Symmetrical components are most commonly used for analysis of three-phase electrical power systems. The voltage or current of a three-phase system at some point can be indicated by three phasors, called the three components of the voltage or the current. This article discusses voltage; however, the same considerations also apply to current.
The horizontal symmetry of the Mandelbrot set allows for portions of the rendering process to be skipped upon the presence of the real axis in the final image. However, regardless of the portion that gets mirrored, the same number of points will be rendered. Julia sets have symmetry around the origin.
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
Glide reflection. A glide reflection is the composition of a reflection across a line and a translation parallel to the line. This footprint trail has glide-reflection symmetry. Applying the glide reflection maps each left footprint into a right footprint and vice versa. In geometry, a glide reflection or transflection is a geometric ...
M. C. Escher: Visions of Symmetry is a book by mathematician Doris Schattschneider published by W. H. Freeman in 1990. The book analyzes the symmetry of M. C. Escher's colored periodic drawings and explains the methods he used to construct his artworks. Escher made extensive use of two-color and multi-color symmetry in his periodic drawings ...
In the first chapter, entitled Patterns with Classical Symmetry, the author introduces the concepts of motif, symmetry operations, lattice and unit cell, and uses these to analyze the symmetry of 13 of Escher's tiling designs. In the second chapter, Patterns with Black-white Symmetry, the antisymmetry operation (indicated by a prime ') is ...
Frieze group. In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. The term is derived from architecture and decorative arts, where such repeating patterns are often used. (See frieze.) Frieze patterns can be classified into seven types according to their symmetries.
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 ...
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