|
Field |
Author |
Description |
| Boys Surface (Bryant and Kusner) |
Geometry |
3D Xplor Math |
The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. |
| Broken Heart |
Fractals |
Jos Leys |
A broken heart created by a variation on a fractal. |
| Different Strokes |
Fractals |
Linda Allison |
Different Strokes is generated with Ultra Fractal, a program designed by Frederik Slijkerman. It consists of 10 layers and uses both Julia and Mandelbrot fractal formulas and other formulas for coloring. |
| Dragons 1 |
Geometry |
Jos Leys |
A tessellation created in the style of M.C. Escher. Escher was famous for his lithographs depicting tessellations or endless loops. Tessellations are images that repeat and seamlessly mesh within one another. Each image alternates color, creating a beautiful and potentially endless work of art. |
| Exp series.gif |
Calculus |
Unknown |
A Taylor series or Taylor polynomial is a series expansion of a function used to approximate its value around a certain point. |
| Fractal Bog |
Fractals |
Jean-Francois Colonna |
This image was obtained by means of a self-transformation of a fractal process. |
| Fractal Scene I |
Fractals |
Anne M. Burns |
"Fractal Scene I" is one of Burns' "Mathscapes" and was created using a variety of mathematical forumluas, including fractal methods to generate the clouds and plant life and vector techniques for the colors. |
| Fun Topology |
Topology |
Paul Nylander |
The topology is equivilent to a sphere with 30 holes. The boundary of each hole loops over itself twice with two Reidemeister-I twists and links with 6 others. |
| Hippopede of Proclus |
Topology |
Adam Coffman |
Consider a torus, T, as a surface of revolution, generated by a circle with radius r > 0, and with center at distance R > 0 from the axis... |
| Hyperbolic Paraboloid |
Calculus |
The Internet |
A hyperbolic paraboloid... |
| Hypercube |
Geometry |
John Baez |
This is an example of a figure that exists in the 4th dimension. It is the dual to the tesseract. It is also the four dimensional figure that is analogous to the three dimensional octahedron. |
| Impossible Geometry |
Geometry |
Lizah Masis |
This image mirrors the depths of artistic creativity combined with mathematical abstractness. M.C. Escher(1898-1972)in this image depicted distorted geometry by presenting infinite planes on a two dimensional plane, making it an impossible reality. If you look closely at the image and imagine being in the house after it has been built, there are a few things you will notice that are not quite right. Imagine standing at one place in the house and watching people move about. At one time, they will be straight up on the floor, but as they climb to higher storeys, it will look like they are walking upside down or on the walls, which is a practical impossibility. Also, although the people climbing the stairs will seem to be ascending, they will actually always remain on the same storey. This image goes beyond the third dimension, showing three different worlds on a two dimensional plane as if they were continuously existing. |
| Indra 432 |
Other |
Jos Leys |
A Kleinian group floating on the water. |
| Inside the Flat (Euclidean) Dodecahedron |
Geometry |
Paul Nylander |
Here is a dodecahedron viewed from the inside with flat mirrored walls. |
| Iterated Functions |
Algebra |
Anna |
|
| Julia Sets |
Fractals |
Anna |
This is a filled Julia Set created with a program described in this page. |
| Klein Bottle |
Geometry |
3DXM Consortium |
The Klein Bottle is a non-orientable surface with no boundary first described in 1882 by the German mathematician Felix Klein. |
| Kleinian Quasifuchsian Limit Set |
Fractals |
Paul Nylander |
Here is a Sunset Moth “blown about” inside a Quasifuchsian limit set. Originally, Felix Klein described these fractals as “utterly unimaginable”, but today we can visualize these fractals with computers. |
| Kummer Quartic |
Algebra |
3DXM Consortium |
A Kummer surface is any one of a one parameter family of algebraic surfaces defined by a specific polynomial equation of degree four. |
| Mateko |
Fractals |
Dan Kuzmenka |
Mateko uses different color palettes than image designer Dan Kuzmenka's usual earth tones. He uses fractals to express a spiral without showing the same shape over again. |
| Mathscape |
Fractals |
Anne M. Burns |
In Mathscape, Burns combines recursive algorithms for clouds, mountains and various imaginary plant forms into one picture. |
| Monkey Saddle |
Calculus |
Mathematica |
The monkey saddle is a surface in Multivariable Calculus that belongs to the class of saddle surfaces. The surface gets its name from the fact that it has three depressions like a saddle for a monkey, which would require two depressions for the legs and one for the monkey's tail. |
| Pretzel Surface |
Algebra |
3DXM Consortium |
The Pretzel surface is an algebraic surface. |
| Quaternion |
|
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| Riemann Sphere |
Algebra |
Unknown |
|
| Siefert surface I |
Algebra |
Jos Leys |
A Seifert surface, a subset of dynamic systems. |
| Skull |
Fractals |
Jos Leys |
An abstract skull created by a variation on a fractal colored to achieve the desired image. |
| Strange plant 1 |
Fractals |
Jos Leys |
A fractal that looks organic in origin, much like a fern or other plant. Fractals reiterate infinitely, and real ferns seem to grow in the same sort of iterative pattern. |
| Tetra 1 |
Geometry |
Jos Leys |
How does one fill a sphere with smaller spheres of various sizes so that every possible void is filled? There are only five known configurations, all obtained by a sphere inversion transformation, the 3D equivalent of a circle inversion. |
| The Regular Hendecachoron |
Geometry |
Carlo Sequin |
This object has 11 vertices (shown as spheres), 55 edges (shown as thin cylindrical beams), and 55 triangular faces (shown as cut-out frames). Different colors indicate triangles belonging to different cells. |
| Torus Knot |
Geometry |
3DXM Consortium |
In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3. |
| Tunnel |
Fractals |
Jos Leys |
A fractal image originating from a Mandelbrot set that Jos Leys created using Ultrafractal. |
| Z-Squared Necklace |
Geometry |
Tom Banchoff |
Each subject is the graph of a function of a complex variable, first the complex squaring operation and then the cubing function... |
