Hausdorff dimension (exact value) 
Hausdorff dimension (approx.) 
Name 
Illustration 
Remarks 
Calculated 
0.538 
Feigenbaum attractorThe logistic map is a polynomial mapping of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations... 

The Feigenbaum attractor (see between arrows) is the set of points generated by successive iterations of the logistic function A logistic function or logistic curve is a common sigmoid curve, given its name in 1844 or 1845 by Pierre François Verhulst who studied it in relation to population growth. It can model the "Sshaped" curve of growth of some population P... for the critical parameter value , where the period doubling is infinite. Notice that this dimension is the same for any differentiable and unimodal function. 

0.6309 
Cantor setIn mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1875 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.... 

Built by removing the central third at each iteration. Nowhere dense and not a countable setIn mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor... . 

0.6942 
Asymmetric Cantor setIn mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1875 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.... 

Note that the dimension is not , as would be expected from the generalized Cantor set with γ=1/4, which has the same length at each stage.
Built by removing the second quarter at each iteration. Nowhere dense and not a countable setIn mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor... .
(golden ratioIn mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989... ). 

0.69897 
Real number In mathematics, a real number is a value that represents a quantity along a continuum, such as 5 , 4/3 , 8.6 , √2 and π... s with even digits 

Similar to a Cantor setIn mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1875 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.... . 

0.88137 
Spectrum of Fibonacci Hamiltonian 

The study the spectrum of the Fibonacci Hamiltonian proves upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that the spectrum converges to an explicit constant. 

0
 Generalized Cantor set 

Built by removing at the th iteration the central interval of length from each remaining segment. At one obtains the usual Cantor setIn mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1875 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.... . Varying between 0 and 1 yields any fractal dimension . 

1 
Smith–Volterra–Cantor set 

Built by removing a central interval of length of each remaining interval at the nth iteration. Nowhere dense but has a Lebesgue measure In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ndimensional Euclidean space. For n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called... of ½. 

1 
Takagi or Blancmange curve 

Defined on the unit interval by , where is the sawtooth function. Special case of the TakahiLandsberg curve: with . The Hausdorff dimension equals for in . (Hunt cited by Mandelbrot ). 
Calculated 
1.0812 
Julia setIn the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function... z² + 1/4 

Julia set for c = 1/4. 

1.0933 
Boundary of the Rauzy fractal thumb300pxRauzy fractalIn mathematics, the Rauzy fractal is a fractal set associated to the Tribonacci substitutionIt has been studied in 1981 by Gérard Rauzy, with the idea of generalizing the dynamic properties of the Fibonacci morphism....


Fractal representation introduced by G.Rauzy of the dynamics associated to the Tribonacci morphism: , and . is one of the conjugated roots of . 

1.12915 
contour of the Gosper island 

Term used by Mandelbrot (1977). The Gosper island is the limit of the Gosper curveThe Gosper curve, named after Bill Gosper, also known as the flowsnake , is a spacefilling curve. It is a fractal object similar in its construction to the dragon curve and the Hilbert curve.... . 
Measured (box counting) 
1.2 
Dendrite Julia setIn the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function... 

Julia set for parameters: Real = 0 and Imaginary = 1. 

1.2083 
Fibonacci word fractal 60° thumb350pxCharacterization by a [[cutting sequence]] with a line of slope 1/\varphi or \varphi1, with \varphi the [[golden ratio]].A Fibonacci word is a specific sequence of binary digits... 

Build from the Fibonacci word thumb350pxCharacterization by a [[cutting sequence]] with a line of slope 1/\varphi or \varphi1, with \varphi the [[golden ratio]].A Fibonacci word is a specific sequence of binary digits... . See also the standard Fibonacci word fractal.
(golden ratioIn mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989... ). 

1.2108 
Boundary of the tame twindragon 

One of the six 2reptile In the geometry of tessellations, a shape that can be dissected into smaller copies of the same shape is called a reptile or reptile. The shape is labelled as repn if the dissection uses n copies... s in the plane (can be tiled by two copies of itself, of equal size). 

1.26 
Hénon map 

The canonical Hénon map (with parameters a = 1.4 and b = 0.3) has Hausdorff dimension 1.261 ± 0.003. Different parameters yield different dimension values. 

1.2619 
Koch curve 

3 von Koch curves form the Koch snowflake or the antisnowflake. 

1.2619 
boundary of Terdragon curve A dragon curve is any member of a family of selfsimilar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.Heighway dragon:... 

Lsystem: same as dragon curve with angle = 30°. The Fudgeflake is based on 3 initial segments placed in a triangle. 

1.2619 
2D Cantor dust 

Cantor set in 2 dimensions. 
Calculated 
1.2683 
Julia setIn the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function... z^{2} − 1 

Julia set for c = −1. 

1.3057 
Apollonian gasketIn mathematics, an Apollonian gasket or Apollonian net is a fractal generated from triples of circles, where each circle is tangent to the other two. It is named after Greek mathematician Apollonius of Perga.Construction:... 

Starting with 3 tangent circles, repeatedly packing new circles into the complementary interstices. Also the limit set generated by reflections in 4 mutually tangent circles. See 
Calculated (Box counting) 
1.328 
5 circles inversion fractal 

The limit set generated by iterated inversions with respect to 5 mutually tangent circles (in red). Also an Apollonian packing. See 
Calculated 
1.3934 
Douady rabbit The Douady rabbit, named for the French mathematician Adrien Douady, is any of various particular filled Julia sets associated with the c near the center period 3 buds of Mandelbrot set for complex quadratic map.Forms of the complex quadratic map:... 

Julia set for c = −0,123 + 0.745i. 

1.4649 
Vicsek fractal 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 carpet. It has applications including as compact antennas, particularly in cellular phones.... 

Built by exchanging iteratively each square by a cross of 5 squares. 

1.4649 
Quadratic von Koch curve (type 1) 

One can recognize the pattern of the Vicsek fractal (above). 
(conjectured exact) 
1.5000 
a Weierstrass functionIn mathematics, the Weierstrass function is a pathological example of a realvalued function on the real line. The function has the property that it is continuous everywhere but differentiable nowhere... : 

The Hausdorff dimension of the Weierstrass function defined by with and has upper bound . It is believed to be the exact value. The same result can be established when, instead of the sine function, we use other periodic functions, like cosine. 

1.5000 
Quadratic von Koch curve (type 2) 

Also called "Minkowski sausage". 

1.5236 
Boundary of the Dragon curve A dragon curve is any member of a family of selfsimilar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.Heighway dragon:... 

cf. Chang & Zhang. 

1.5236 
Boundary of the twindragon curve A dragon curve is any member of a family of selfsimilar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.Heighway dragon:...


Can be built with two dragon curves. One of the six 2reptile In the geometry of tessellations, a shape that can be dissected into smaller copies of the same shape is called a reptile or reptile. The shape is labelled as repn if the dissection uses n copies... s in the plane (can be tiled by two copies of itself, of equal size). 

1.5849 
3branches tree 

Each branch carries 3 branches (here 90° and 60°). The fractal dimension of the entire tree is the fractal dimension of the terminal branches. NB: the 2branches tree has a fractal dimension of only 1. 

1.5849 
Sierpinski triangleThe Sierpinski triangle , also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13thcentury Cosmati mosaics in the cathedral... 

Also the triangle of Pascal modulo 2. 

1.5849 
Sierpiński arrowhead curveThe Sierpiński arrowhead curve is a fractal curve similar in appearance and identical in limit to the Sierpiński triangle.Representation as Lindenmayer system:The Sierpiński arrowhead curve can be expressed by a rewrite system .Literature:... 

Same limit as the triangle (above) but built with a onedimensional curve. 

1.5849 
Boundary of the TSquareIn mathematics, the Tsquare is a twodimensional fractal. As all twodimensional fractals, it has a boundary of infinite length bounding a finite area... fractal 



1.61803 
a golden dragon A dragon curve is any member of a family of selfsimilar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.Heighway dragon:... 

Built from two similarities of ratios and , with . Its dimension equals because . With (Golden number Golden number may mean:* Golden number , a number assigned to a calendar year denoting its place in a Metonic cycle* Golden ratio, an irrational mathematical constant with special properties in arts and mathematics... ). 

1.6309 
Pascal triangle modulo 3 

For a triangle modulo k, if k is prime, the fractal dimension is (cf. Stephen WolframStephen Wolfram is a British scientist and the chief designer of the Mathematica software application and the Wolfram Alpha computational knowledge engine. Biography :... ). 

1.6309 
Sierpinski Hexagon 

Built in the manner of the Sierpinski carpet The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions . Sierpiński demonstrated that this fractal is a universal curve, in that any possible onedimensional graph, projected onto the twodimensional... , on an hexagonal grid, with 6 similitudes of ratio 1/3. Notice the presence of the Koch snowflakeThe Koch snowflake is a mathematical curve and one of the earliest fractal curves to have been described... at all scales. 

1.6379 
Fibonacci word fractal thumb350pxCharacterization by a [[cutting sequence]] with a line of slope 1/\varphi or \varphi1, with \varphi the [[golden ratio]].A Fibonacci word is a specific sequence of binary digits... 

Fractal based on the Fibonacci word thumb350pxCharacterization by a [[cutting sequence]] with a line of slope 1/\varphi or \varphi1, with \varphi the [[golden ratio]].A Fibonacci word is a specific sequence of binary digits... (or Rabbit sequence) Sloane A005614. Illustration : Fractal curve after 23 steps (F_{23} = 28657 segments). (golden ratioIn mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989... ). 
Solution of 
1.6402 
Attractor of IFS In mathematics, iterated function systems or IFSs are a method of constructing fractals; the resulting constructions are always selfsimilar.... with 3 similaritiesTwo geometrical objects are called similar if they both have the same shape. More precisely, either one is congruent to the result of a uniform scaling of the other... of ratios 1/3, 1/2 and 2/3 

Generalization : Providing the open set condition holds, the attractor of an iterated function system In mathematics, iterated function systems or IFSs are a method of constructing fractals; the resulting constructions are always selfsimilar.... consisting of similarities of ratios , has Hausdorff dimension , solution of the equation : . 

1.6826 
Pascal triangle modulo 5 

For a triangle modulo k, if k is prime, the fractal dimension is (cf. Stephen WolframStephen Wolfram is a British scientist and the chief designer of the Mathematica software application and the Wolfram Alpha computational knowledge engine. Biography :... ). 
Measured (boxcounting) 
1.7 
Ikeda map attractor 

For parameters a=1, b=0.9, k=0.4 and p=6 in the Ikeda map . It derives from a model of the planewave interactivity field in an optical ring laser. Different parameters yield different values. 

1.7227 
Pinwheel fractal Pinwheel tilings are nonperiodic tilings defined by Charles Radin and based on a construction due to John Conway.They are the first known nonperiodic tilings to each have the property that their tiles appear in infinitely many orientations.... 

Built with Conway's Pinwheel tile. 

1.7712 
Hexaflake A hexaflake is a fractal constructed by iteratively exchanging each hexagon by a flake of seven hexagons; it is a special case of the nflake. As such, a hexaflake would have 7n1 hexagons in its nth iteration. Its boundary is the von Koch flake, and contains an infinite number of Koch snowflakes... 

Built by exchanging iteratively each hexagon by a flake of 7 hexagons. Its boundary is the von Koch flake and contains an infinity of Koch snowflakes (black or white). 

1.7848 
Von Koch curve 85° 

Generalizing the von Koch curve with an angle a chosen between 0 and 90°. The fractal dimension is then . 

1.8272 
A selfaffine In geometry, an affine transformation or affine map or an affinity is a transformation which preserves straight lines. It is the most general class of transformations with this property... fractal set 

Build iteratively from a array on a square, with . Its Hausdorff dimension equals with and is the number of elements in the column. The boxcounting dimension yields a different formula, therefore, a different value. Unlike selfsimilar sets, the Hausdorff dimension of selfaffine sets depends on the position of the iterated elements and there is no formula, so far, for the general case. 

1.8617 
Pentaflake 

Built by exchanging iteratively each pentagon by a flake of 6 pentagons.
(golden ratioIn mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989... ). 
solution of 
1.8687 
Monkeys tree 

This curve appeared in Benoit MandelbrotBenoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child... 's "Fractal geometry of Nature" (1983). It is based on 6 similarities of ratio and 5 similarities of ratio . 

1.8928 
Sierpinski carpet The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions . Sierpiński demonstrated that this fractal is a universal curve, in that any possible onedimensional graph, projected onto the twodimensional... 

Each face of the Menger sponge is a Sierpinski carpet, as is the bottom surface of the 3D quadratic Koch surface (type 1). 

1.8928 
3D Cantor dust 

Cantor set in 3 dimensions. 


Cartesian product of the von Koch curve and the Cantor setIn mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1875 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.... 

Generalization : Let FxG be the cartesian product of two fractals sets F and G. Then . See also the 2D Cantor dust and the Cantor cube. 
Estimated 
1.9340 
Boundary of the Lévy C curveIn mathematics, the Lévy C curve is a selfsimilar fractal that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and G... 

Estimated by Duvall and Keesling (1999). The curve itself has a fractal dimension of 2. 

1.974 
Penrose tiling A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original... 

See Ramachandrarao, Sinha & Sanyal. 

2 
Boundary of the Mandelbrot set The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable twodimensional fractal shape... 

The boundary and the set itself have the same dimension. 

2 
Julia setIn the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function... 

For determined values of c (including c belonging to the boundaryA Misiurewicz point is a parameter in the Mandelbrot set for which the critical point is strictly preperiodic . By analogy, the term Misiurewicz point is also used for parameters in a Multibrot set where the unique critical point is strictly preperiodic... of the Mandelbrot set), the Julia set has a dimension of 2. 

2 
Sierpiński curveSierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit n \rightarrow \infty completely fill the unit square: thus their limit curve, also called the Sierpiński curve, is an example of a spacefilling... 

Every Peano curve filling the plane has a Hausdorff dimension of 2. 

2 
Hilbert curve A Hilbert curve is a continuous fractal spacefilling curve first described by the German mathematician David Hilbert in 1891, as a variant of the spacefilling curves discovered by Giuseppe Peano in 1890.... 



2 
Peano curve 

And a family of curves built in a similar way, such as the Wunderlich curves. 

2 
Moore curveA Moore curve is a continuous fractal spacefilling 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 the union of four copies of the Hilbert curves combined in such a way to make the endpoints coincide.Because the Moore... 

Can be extended in 3 dimensions. 

2 
Lebesgue curve or zorder curve In mathematical analysis and computer science, Zorder, Morton order, or Morton code is a spacefilling curve which maps multidimensional data to one dimension while preserving locality of the data points. It was introduced in 1966 by G. M. Morton... 

Unlike the previous ones this spacefilling curve is differentiable almost everywhere. Another type can be defined in 2D. Like the Hilbert Curve it can be extended in 3D. 

2 
Dragon curve A dragon curve is any member of a family of selfsimilar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.Heighway dragon:... 

And its boundary has a fractal dimension of 1.5236270862. 

2 
Terdragon curve A dragon curve is any member of a family of selfsimilar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.Heighway dragon:... 

Lsystem: F → F + F – F, angle = 120°. 

2 
Gosper curveThe Gosper curve, named after Bill Gosper, also known as the flowsnake , is a spacefilling curve. It is a fractal object similar in its construction to the dragon curve and the Hilbert curve.... 

Its boundary is the Gosper island. 
Solution of 
2 
Curve filling the Koch snowflake The Koch snowflake is a mathematical curve and one of the earliest fractal curves to have been described... 

Proposed by Mandelbrot in 1982, it fills the Koch snowflake The Koch snowflake is a mathematical curve and one of the earliest fractal curves to have been described... . It is based on 7 similarities of ratio 1/3 and 6 similarities of ratio . 

2 
Sierpiński tetrahedronThe Sierpinski triangle , also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13thcentury Cosmati mosaics in the cathedral... 

Each tetrahedronIn geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids... is replaced by 4 tetrahedra. 

2 
Hfractal 

Also the Mandelbrot tree which has a similar pattern. 


Pythagoras tree (fractal) 

Every square generates two squares with a reduction ratio of sqrt(2)/2. 

2 
2D Greek cross fractal 

Each segment is replaced by a cross formed by 4 segments. 
Measured 
2.01 ±0.01 
Rössler attractor The Rössler attractor is the attractor for the Rössler system, a system of three nonlinear ordinary differential equations. These differential equations define a continuoustime dynamical system that exhibits chaotic dynamics associated with the fractal properties of the attractor... 

The fractal dimension of the Rössler attractor is slightly above 2. For a=0.1, b=0.1 and c=14 it has been estimated between 2.01 and 2.02. 
Measured 
2.06 ±0.01 
Lorenz attractor The Lorenz attractor, named for Edward N. Lorenz, is an example of a nonlinear dynamic system corresponding to the longterm behavior of the Lorenz oscillator. The Lorenz oscillator is a 3dimensional dynamical system that exhibits chaotic flow, noted for its lemniscate shape... 

For parameters v=40,=16 and b=4 . See McGuinness (1983) 

2.3219 
Fractal pyramid 

Each pyramid is replaced by 5 pyramids, twice smaller. Must not be confused with the Sierpinski tetrahedron, since it is based on a square pyramid. 

2.3296 
Dodecahedron fractal 

Each dodecahedron is replaced by 20 dodecahedra.
(golden ratioIn mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989... ). 

2.3347 
3D quadratic Koch surface (type 1) 

Extension in 3D of the quadratic Koch curve (type 1). The illustration shows the second iteration. 

2.4739 
Apollonian sphere packing Apollonian sphere packing is the three dimensional equivalent of the Apollonian gasket. The principle of construction is very similar: with any four spheres that are cotangent to each other, it is then possible to construct two more spheres that are cotangent to four of them.The fractal dimension... 

The interstice left by the Apollonian spheres. Apollonian gasket in 3D. Dimension calculated by M. Borkovec, W. De Paris, and R. Peikert. 

2.50 
3D quadratic Koch surface (type 2) 

Extension in 3D of the quadratic Koch curve (type 2). The illustration shows the second iteration. 

2.5237 
Cantor tesseract 
no image available 
Cantor set in 4 dimensions. Generalization: in a space of dimension n, the Cantor set has a Hausdorff dimension of . 

2.5819 
Icosahedron fractal 

Each icosahedronIn geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids.... is replaced by 12 icosahedra. (golden ratioIn mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989... ). 

2.5849 
3D Greek cross fractal 

Each segment is replaced by a cross formed by 6 segments. 

2.5849 
Octahedron fractal 

Each octahedronIn geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.... is replaced by 6 octahedra. 

2.5849 
von Koch surface 

Each equilateral triangular face is cut into 4 equal triangles.
Using the central triangle as the base, form a tetrahedron. Replace the triangular base with the tetrahedral "tent". 

2.7268 
Menger spongeIn mathematics, the Menger sponge is a fractal curve. It is a universal curve, in that it has topological dimension one, and any other curve is homeomorphic to some subset of it. It is sometimes called the MengerSierpinski sponge or the Sierpinski sponge... 

And its surface has a fractal dimension of , which is the same as that by volume. 

3 
3D Hilbert curve A Hilbert curve is a continuous fractal spacefilling curve first described by the German mathematician David Hilbert in 1891, as a variant of the spacefilling curves discovered by Giuseppe Peano in 1890.... 

A Hilbert curve extended to 3 dimensions. 

3 
3D Lebesgue curve In mathematical analysis and computer science, Zorder, Morton order, or Morton code is a spacefilling curve which maps multidimensional data to one dimension while preserving locality of the data points. It was introduced in 1966 by G. M. Morton... 

A Lebesgue curve extended to 3 dimensions. 

3 
3D Moore curveA Moore curve is a continuous fractal spacefilling 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 the union of four copies of the Hilbert curves combined in such a way to make the endpoints coincide.Because the Moore... 

A Moore curve extended to 3 dimensions. 

3 
3D Hfractal 

A Hfractal extended to 3 dimensions. 


Mandelbulb The Mandelbulb is a threedimensional analogue of the Mandelbrot set, constructed by Daniel White and Paul Nylander using spherical coordinates.... 

Extension of the Mandelbrot set (power 8) in 3 dimensions 