A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal.[1] In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length.[2]
A famous example is the boundary of the Mandelbrot set.
A fractalcurve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified...
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding...
Koch curve, Koch star, or Koch island) is a fractalcurve and one of the earliest fractals to have been described. It is based on the Koch curve, which...
A dragon curve is any member of a family of self-similar fractalcurves, which can be approximated by recursive methods such as Lindenmayer systems. The...
For instance, a curve with a fractal dimension very near to 1, say 1.10, behaves quite like an ordinary line, but a curve with fractal dimension 1.9 winds...
known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractalcurve. It is a three-dimensional generalization of...
mathematics, the blancmange curve is a self-affine fractalcurve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi...
Knecht, R. Ziff, to be published Monkeys tree fractalcurve Archived 21 September 2002 at archive.today Fractal dimension of a Penrose tiling Shishikura,...
continuous everywhere but differentiable nowhere. It is an example of a fractalcurve. It is named after its discoverer Karl Weierstrass. The Weierstrass...
magnifications; mathematically, the boundary of the Mandelbrot set is a fractalcurve. The "style" of this recursive detail depends on the region of the set...
In mathematics, a de Rham curve is a continuous fractalcurve obtained as the image of the Cantor space, or, equivalently, from the base-two expansion...
space-filling curves and fractalcurves. For ensuring more regularity, the function that defines a curve is often supposed to be differentiable, and the curve is...
limit set is rep-7. It is a fractalcurve similar in its construction to the dragon curve and the Hilbert curve. The Gosper curve can also be used for efficient...
solving non-linear equations or polynomial equations. Fractals are any of various extremely irregular curves or shapes for which any suitably chosen part is...
The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician...
length. This results from the fractalcurve–like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension. Although the "paradox...
curve De Rham curve Dragon curve Koch curve Lévy C curve Sierpiński curve Space-filling curve (Peano curve) See also List of fractals by Hausdorff dimension...
The Minkowski sausage or Minkowski curve is a fractal first proposed by and named for Hermann Minkowski as well as its casual resemblance to a sausage...
given total surface area or volume. Such fractal antennas are also referred to as multilevel and space filling curves, but the key aspect lies in their repetition...
In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, is a fractal arising from a construction similar to that of the Sierpinski...
The Fibonacci word fractal is a fractalcurve defined on the plane from the Fibonacci word. This curve is built iteratively by applying the Odd–Even Drawing...
every year from electrocution. Crown shyness Dielectric breakdown model Fractalcurve Kirlian photography Lightning burn Patterns in nature Diffusion-limited...
infinite perimeters, and can have infinite or finite areas. One such fractalcurve with an infinite perimeter and finite area is the Koch snowflake.[citation...
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