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The usage of the word "gasket" to refer to the Sierpiński triangle refers to gaskets such as are found in motors, and which sometimes feature a series of holes of decreasing size, similar to the fractal; this usage was coined by Benoit Mandelbrot, who thought the fractal looked similar to "the part that prevents leaks in motors". [23]
Animated creation of a Sierpinski triangle using a chaos game method The way the "chaos game" works is illustrated well when every path is accounted for.. In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it.
Sierpiński demonstrated that this fractal is a universal curve, in that any possible one-dimensional graph, projected onto the two-dimensional plane, is homeomorphic to a subset of the Sierpinski gasket. For curves that cannot be drawn on a 2D surface without self-intersections, the corresponding universal curve is the Menger sponge.
An n-flake, polyflake, or Sierpinski n-gon, [1]: 1 is a fractal constructed starting from an n-gon. This n-gon is replaced by a flake of smaller n-gons, such that the scaled polygons are placed at the vertices, and sometimes in the center. This process is repeated recursively to result in the fractal.
Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit completely fill the unit square: thus their limit curve, also called the Sierpiński curve, is an example of a space-filling curve.
Fractal fern in four states of construction. Highlighted triangles show how the half of one leaflet is transformed to half of one whole leaf or frond.. Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands, which makes use of a computer practically mandatory.
An aerial view of the Kayenta Solar Plant in Kayenta, Arizona, part of a project backed by the Department of Energy to bring clean power to communities off the main electrical grid.
The prior art includes an RF MEMS frequency tunable fractal antenna for the 0.1–6 GHz frequency range, [18] and the actual integration of RF MEMS switches on a self-similar Sierpinski gasket antenna to increase its number of resonant frequencies, extending its range to 8 GHz, 14 GHz and 25 GHz, [19] [20] an RF MEMS radiation pattern ...