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The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
Burning Ship fractal. Detail of the Burning Ship fractal. The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function: in the complex plane which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set is ...
But in measuring an infinitely "wiggly" fractal curve such as the Koch snowflake, one would never find a small enough straight segment to conform to the curve, because the jagged pattern would always re-appear, at arbitrarily small scales, essentially pulling a little more of the tape measure into the total length measured each time one ...
The columns interpreted as binary numbers give 1, 3, 5, 15, 17, 51... (sequence A001317 in the OEIS) The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this ...
An object whose irregularity is constant over different scales ("self-similarity") is a fractal (examples include the Menger sponge, the Sierpiński gasket, and the Koch curve or snowflake, which is infinitely long yet encloses a finite space and has a fractal dimension of circa 1.2619).
The stellated octahedron is the first iteration of the 3D analogue of a Koch snowflake. A compound of two spherical tetrahedra can be constructed, as illustrated. The two tetrahedra of the compound view of the stellated octahedron are "desmic", meaning that (when interpreted as a line in projective space ) each edge of one tetrahedron crosses ...
It's safe to say that Monsters has changed Nicholas Alexander Chavez's life.. The actor, 25, stars as Lyle Menendez alongside Cooper Koch's Erik in Monsters: The Lyle and Erik Menendez Story ...
Vicsek fractal. Vicsek fractal (5th iteration of cross form) In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, [1][2] is a fractal arising from a construction similar to that of the Sierpiński carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones.