Category: Fractal curves

Gosper curve
The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the flowsnake (a spoonerism of snowflake), is a space-filling curve whose limit set is rep-7. It is a fractal curve
Fibonacci word fractal
The Fibonacci word fractal is a fractal curve defined on the plane from the Fibonacci word.
An n-flake, polyflake, or Sierpinski n-gon, 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 vertic
Moore curve
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 of the Hilbert curve, and it may be thought as
Singular function
In mathematics, a real-valued function f on the interval [a, b] is said to be singular if it has the following properties: * f is continuous on [a, b]. (**) * there exists a set N of measure 0 such
Dragon curve
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 dragon curve is probably most commonly thought
Weierstrass function
In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its di
Peano curve
In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit interval onto t
List of fractals by Hausdorff dimension
According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension."Presented here is a list of fractals, ordere
Sierpiński curve
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 cur
Z-order curve
In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve, Morton order or Morton code map multidimensional data to one dimension while pre
Fractal curve
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.
Hilbert curve
The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the spa
Space-filling curve
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an n-dimensional unit hypercube). Because Giuseppe Peano (1858–1