A fractal curve 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 fractal curve 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 fractal curves, 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...

increase without bound. Space-filling curves are special cases of fractal curves. No differentiable space-filling curve can exist. Roughly speaking, differentiability...

mathematics, the blancmange curve is a self-affine fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi...

continuous everywhere but differentiable nowhere. It is also an example of a fractal curve. The Weierstrass function has historically served the role of a pathological...

In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto...

known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of...

Knecht, R. Ziff, to be published Monkeys tree fractal curve Archived 21 September 2002 at archive.today Fractal dimension of a Penrose tiling Shishikura,...

Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit n →...

In mathematics, a de Rham curve is a continuous fractal curve obtained as the image of the Cantor space, or, equivalently, from the base-two expansion...

magnifications; mathematically, the boundary of the Mandelbrot set is a fractal curve. The "style" of this recursive detail depends on the region of the set...

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 fractal curve-like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension. Although the "paradox...

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 Sierpiński...

The Fibonacci word fractal is a fractal curve defined on the plane from the Fibonacci word. This curve is built iteratively by applying the Odd–Even Drawing...

solving non-linear equations or polynomial equations. Fractals are any of various extremely irregular curves or shapes for which any suitably chosen part is...

space-filling curves and fractal curves. For ensuring more regularity, the function that defines a curve is often supposed to be differentiable, and the curve is...

Following is a list of shapes studied in mathematics. Cubic plane curve Quartic plane curve Fractal Conic sections Unit circle Unit hyperbola Folium of Descartes...

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...

Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both...

A Moore curve (after E. H. Moore) is a continuous fractal space-filling curve which is a variant of the Hilbert curve. Precisely, it is the loop version...

limit set is rep-7. It is a fractal curve similar in its construction to the dragon curve and the Hilbert curve. The Gosper curve can also be used for efficient...

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...

is the von Koch curve of varying types – depending on the n-gon – and infinitely many Koch curves are contained within. The fractals occupy zero area...

phenomenon of inaccuracies caused by pixelation Cantor staircase, a fractal curve along the diagonal of a unit square Taxicab geometry, in which the lengths...

Dimension theory Dragon curve Fatou set Fractal Fractal antenna Fractal art Fractal compression Fractal flame Fractal landscape Fractal transform Fractint...

infinite perimeters and can have infinite or finite areas. One such fractal curve with an infinite perimeter and finite area is the Koch snowflake. Leopold...