Math Image Slideshow

All Images

A Complex Number

Field: Algebra
Details: We visualize complex numbers in the same way we visualize an ordered pair on a plane.

Blue Fern

Field: Algebra
Details: The Blue Fern is a fractal, similar to Barnsley's Fern fractal that was created by Michael Barnsley using an iterated function system.

Vector Field of a Fluid

Field: Algebra
Details: The vector field shown here represents the velocity of a fluid. Each vector represents the fluid's velocity at the point the arrow begins.

Projection of a 4-Dimensional Torus

Field: Algebra
Details: A torus in four dimensions projected into three-dimensional space.

Hyperboloid

Field: Calculus
Details: A hyperboloid is a quadric, a type of surface in three dimensions.

Butterfly Curve

Field: Calculus
Details: The Butterfly Curve is one of many beautiful images generated using parametric equations.

Harmonic Warping of Blue Wash

Field: Calculus
Details: This image is a tiling based on harmonic warping operations. These operations take a source image and compress it to show the infinite tiling of the source image within a finite space.

Fountain Flux

Field: Calculus
Details: The water flowing out of a fountain demonstrates an important theorem for vector fields, the Divergence Theorem.

Solid of revolution

Field: Calculus
Details: This image is a solid of revolution

Change of Coordinates

Field: Calculus
Details: The same object, here a disk, can look completely different depending on which coordinate system is used.

Harter-Heighway Dragon Curve

Field: Dynamic Systems
Details: This image is an artistic rendering of the Harter-Heighway Curve (also called the Dragon Curve), which is a fractal. It is often referred to as the Jurassic Park Curve because it garnered popularity after being drawn and alluded to in the novel Jurassic Park by Michael Crichton (1990).

Henon Attractor

Field: Dynamic Systems
Details: This image is a Henon Attractor (named after astronomer and mathematician Michel Henon), which is a fractal in the division of the chaotic strange attractor.

Sol-Koch

Field: Fractals
Details: The image is an example of a Koch Snowflake, a fractal that first appeared in a paper by Swede Niels Fabian Helge von Koch in 1904. It is made by the infinite iteration of the Koch curve.

Blue Wash

Field: Fractals
Details: This image is a random fractal that is created by continually dividing a rectangle into two parts and adjusting the brightness of each resulting part.

Newton's Basin

Field: Fractals
Details: Newton's Basin is a visual representation of Newton's Method, which is a procedure for estimating the root of a function.

A Julia Set

Field: Fractals
Details: This is a filled Julia Set created with a program described in this page.

Tiling of the Alhambra

Field: Geometry

Roulette

Field: Geometry
Details: Four different roulettes formed by rolling four different shapes and tracing a fixed point on each of these shapes.

Catenary

Field: Geometry
Details: A catenary is the curve created by a theoretical representation of a hanging chain or cable held at both ends.

Parabola

Field: Geometry
Details: A parabola is a u-shaped curve that arises not only in the field of mathematics, but also in many other fields such as physics and engineering.

Sierpinski's triangle

Field: Geometry
Details: Sierpinski's triangle is a simple fractal created by repeatedly removing smaller triangles from the original shape.

Parabolic Reflector Dish

Field: Geometry
Details: Solar Dishes such as the one shown use a parabolic shape to focus the incoming light into a single collector.

Hyperbolic Tilings

Field: Geometry
Details: This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles.

Hyperbolic Geometry

Field: Geometry
Details: This is an animation of a square rotating in hyperbolic geometry as represented by the Poincaré Disk Model.

Seven Bridges of Königsberg

Field: Graph Theory
Details: The Seven Bridges of Königsberg is a historical problem that illustrates the foundations of Graph Theory

Four Color Theorem

Field: Graph Theory
Details: This image shows a four coloring and graph representation of the United States.

Chryzode

Field: Number Theory
Details: Chryzodes are visualizations of arithmetic using chords in a circle.

Mobius Strip

Field: Topology
Details: A Mobius strip, also referred to as a Mobius band, is a surface with only one side and one edge.

Algebra