All Images
Seifert surface
Author: Jos Leys Field: Algebra
Details: A Seifert surface, a subset of dynamic systems.
Kummer Quartic
Author: 3DXM Consortium Field: Algebra
Details: A Kummer surface is any one of a one parameter family of algebraic surfaces defined by a specific polynomial equation of degree four.
Pretzel Surface
Author: 3DXM Consortium Field: Algebra
Details: The Pretzel surface is an algebraic surface.
2-sphere wireframe
Author: Unknown Field: Calculus
Details: This is a wireframe rendering of a 3 dimensional sphere.
Hyperboloid
Author: Paul Nylander Field: Calculus
Details: A hyperboloid is a quadric, a type of surface in three dimensions.
Different Strokes
Author: Linda Allison Field: Fractals
Details: 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.
Mateko
Author: Dan Kuzmenka Field: Fractals
Details: 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.
Fractal Scene I
Author: Anne M. Burns Field: Fractals
Details: "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.
Tunnel
Author: Jos Leys Field: Fractals
Details: A fractal image originating from a Mandelbrot set that Jos Leys created using Ultrafractal.
Broken Heart
Author: Jos Leys Field: Fractals
Details: A broken heart created by a variation on a fractal.
Skull
Author: Jos Leys Field: Fractals
Details: An abstract skull created by a variation on a fractal colored to achieve the desired image.
Strange Plant 1
Author: Jos Leys Field: Fractals
Details: 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.
Fractal Bog
Author: Jean-Francois Colonna Field: Fractals
Details: This image was obtained by means of a self-transformation of a fractal process.
Mountains In Spring
Author: Anne M. Burns Field: Fractals
Details: One of Anne Burns' Mathscapes, the plant life in "Mountains in Spring" were generated using fractal methods.
Kleinian Quasifuchsian Limit Set
Author: Paul Nylander Field: Fractals
Details: 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.
Mathscape
Author: Anne M. Burns Field: Fractals
Details: In Mathscape, Burns combines recursive algorithms for clouds, mountains and various imaginary plant forms into one picture.
Romanesco broccoli
Author: Jon Sullivan Field: Fractals
Details: Fractals appear in nature, and the Romanesco broccoli is a particularly obvious instance. Along with the fern, the surface of the Romanesco broccoli appears to arise from a fractal reiterated many times.
Mandelbrot Set 1
Author: António Miguel de Campos Field: Fractals
Details: An example of a Mandelbrot set. The spiral appears to continue infinitely with each iteration. The spiral will get more detailed the more the viewer zooms in, until the viewer appears to be seeing what he or she began with.
Z-Squared Necklace
Author: Tom Banchoff Field: Geometry
Details: Each subject is the graph of a function of a complex variable, first the complex squaring operation and then the cubing function...
Tetra 1
Author: Jos Leys Field: Geometry
Details: 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.
Dragons 1
Author: Jos Leys Field: Geometry
Details: 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.
Inside the Flat (Euclidean) Dodecahedron
Author: Paul Nylander Field: Geometry
Details: Here is a dodecahedron viewed from the inside with flat mirrored walls.
The Regular Hendecachoron
Author: Carlo Sequin Field: Geometry
Details: 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
Author: 3DXM Consortium Field: Geometry
Details: In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3.
Frabjous
Author: George W. Hart Field: Other
Details: Frabjous is a sculpture created by George W. Hart from laser cut aspen wood. The sculpture is constructed from elongated s-curve pieces that, when fitted together, create a swirling vortex.
Algebra
Seifert surface
Author: Jos Leys Field: Algebra
Details: A Seifert surface, a subset of dynamic systems.
Calculus
Fractals
Different Strokes
Author: Linda Allison Field: Fractals
Details: 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.
Mateko
Author: Dan Kuzmenka Field: Fractals
Details: 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.
Fractal Scene I
Author: Anne M. Burns Field: Fractals
Details: "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.
Tunnel
Author: Jos Leys Field: Fractals
Details: A fractal image originating from a Mandelbrot set that Jos Leys created using Ultrafractal.
Broken Heart
Author: Jos Leys Field: Fractals
Details: A broken heart created by a variation on a fractal.
Skull
Author: Jos Leys Field: Fractals
Details: An abstract skull created by a variation on a fractal colored to achieve the desired image.
Strange Plant 1
Author: Jos Leys Field: Fractals
Details: 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.
Fractal Bog
Author: Jean-Francois Colonna Field: Fractals
Details: This image was obtained by means of a self-transformation of a fractal process.
Mountains In Spring
Author: Anne M. Burns Field: Fractals
Details: One of Anne Burns' Mathscapes, the plant life in "Mountains in Spring" were generated using fractal methods.
Kleinian Quasifuchsian Limit Set
Author: Paul Nylander Field: Fractals
Details: 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.
Mathscape
Author: Anne M. Burns Field: Fractals
Details: In Mathscape, Burns combines recursive algorithms for clouds, mountains and various imaginary plant forms into one picture.
Geometry
Z-Squared Necklace
Author: Tom Banchoff Field: Geometry
Details: Each subject is the graph of a function of a complex variable, first the complex squaring operation and then the cubing function...
Tetra 1
Author: Jos Leys Field: Geometry
Details: 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.
Dragons 1
Author: Jos Leys Field: Geometry
Details: 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.
Inside the Flat (Euclidean) Dodecahedron
Author: Paul Nylander Field: Geometry
Details: Here is a dodecahedron viewed from the inside with flat mirrored walls.