Infinite families of tangent circles. More here

Pickover's Popcorn fractal rendered using a triangular variation of the Hilbert space-filling curve.
By Kerry Mitchell

Visualizing Conformal Mapping

Beautiful works by Samuel Monnier visually exploring the Lattès map
  

Limit set

Limit set of a group determined by a thrice punctured sphere
By David Dumas

Twin Snowflakes

     "Since each snowflake faces a different turbulent path through the atmosphere, each twist, turn and fall grants it a unique symmetry. But if you subtract nature’s volatility from the equation, then these icy flowers are no longer guaranteed uniqueness.

     By placing two crystal seeds next to each other and growing them under the exact same conditions, Dr. Libbrecht found that he could create two snowflakes with nearly the same intricate shapes and patterns."

Twin snowflakes, grown from crystals under the same temperature and humidity conditions, surrounded by water droplets.  (Kenneth Libbrech)

new record for largest skydiving formation - 202 people

Multiplication table mod 512

John Conway's Game of Life

jump to 1:55

Primitive Pythagorean Triples

"The shapes are are nodes of a twisted torus knot. In producing the model, surface normals were reversed to maintain color interest and mathematical harmony. A torus knot is a knot that lies on the surface of an unknotted torus in R3."
By Harry Benke

"This image is produced by applying Newton's method for root finding to the complex function (z^(2+3i)-.09)*(z^(2-3i) -.09).The white areas are points in the complex plane where this function does not converge to any root. The background is produced using Perlin noise functions."

"This image is produced by iterating the complex polynomial (z^2-2)/z^2. This complex polynomial has no attracting fixed points in the complex plane."

By Robert Spann

Light sculptures by Diet Wiegman

 

 

It's awesome how two different projections of a 3-dimensional object onto a 2-dimensional plane can look nothing alike. I like that in each of these pictures we're looking at both projections at once.

How locks work

"Artist Jonty Hurwitz makes anamorphic sculptures that at first glance appear abstract, but when viewed in a certain way, reveal distinct forms. To create the effect, Hurwitz scans objects and then distorts them using 3D software and quite a lot of math. The completed sculptures can then be viewed undistorted using mirrored cylinders or from very specific angles."

"When a magnitude 6.8 earthquake shook Olympia, Wash., in 2001, shopowner Jason Ward discovered that a sand-tracing pendulum had recorded the vibrations in the image above."

Forty billion particles evolve under their own gravity. More here.

"The object was generated with 7 million triangles, simplified to 1 million for export and rendered with Indigo."

"The artist creates the basic idea of the picture (plot, esthetics), basic colours, basic principles of their development. Then a computer works on the picture's individuality, adding more variations and fluctuations of the basic elements and letting them develop with time: the picture living its own life with objects moved and transformed but still following the original artist's concept." Sam Base

Michael Sussna's geometric scenery

Paul Nylander creates a double spiral by applying a light projection from the top of a loxodrome onto a plane.

"A picture of a 428x428 Hadamard matrix, i.e. a matrix with orthogonal columns and all entries equal to +1 (white pixels) or -1 (black pixels). This example was discovered by H. Kharaghani and B. Tayfeh-Rezaie in 2004, and was the first of size 428x428. It is not known if there is a 668x668 Hadamard matrix, though it is conjectured that examples of size 4n x 4n exist for all n."

John Baez uses Category Theory (an abstraction of what is already very abstract math) to answer important questions in physics.

Early computer graphics from 1961-1962 by Herbert W. Franke

Embers by TDA "Doing spectacular things with very little code has a long tradition in the demoscene. Born out of necessity when home computers were slow and memory space scarce, pushing against artificial boundaries became a popular “sport” when PC hardware power blew up. Time and again we’ve seen demosceners tighten the limits in search of a good challenge and do voodoo with 64 and even 4 kilobytes. At the recent edition of Assembly, a demoscene main event in Helsinki (Finland) with a 20 year history, this race for minimal footprint has reached a new low: 1 kilobyte (1024 bytes) or less! While technically 1k (and smaller) intros are nothing new, Assembly’s first ever “1 kilobyte intro competition” marks a breakthrough for the category."

"Hartverdrahtet by Akronyme Analogiker is a three minute long audio-visual trip into a procedural fractalverse, compressed into a minuscule piece of software. No bigger than 4096 bytes – less than an empty Word document, as demoscene activists like to point out – the executable file contains all the mathematics needed to generate the unfolding visual complexity and audible ambience upon a double-click."

Generative Art by Andreas Fischer

Voronoi diagram by Diana Lange

Hacking a TV with an electromagnet. Click here for a how to.

Oscillation Number Four - Electronic Abstraction by Ben Laposky(1950) “Oscillations were the first graphics made on an analog computer. For many years, they represented the most advanced acheivements of what was known as computer art. His oscillations are photographs of electronic wave forms displayed on a cathode-ray tube. Hardware: oscilloscope with sine wave generators”

These underwater “crop circles” were until recently a complete mystery. Japanese underwater photographer Yoji Ookata discovered the intricate 6 foot wide circles on the seafloor off Amami Oshima island in Japan. He returned to the island with an NHK film crew in order to study the circles. Together they discovered the artist behind the circles—a small species of pufferfish. Males of the species create the circles with their fins in order to attract females. They mate in the center and the circle helps keep the eggs from drifting away.

By Salvatore Musumeci

This is a circle formed from intersecting chords of a larger circle

Schlegel diagram for the truncated 120-cell with tetrahedral cells

A ferrofluid droplet under the influence of a vertical magnetic field.

"The magnetosphere is shaped somewhat like a comet due to pressure of the solar wind. It is compressed on the side toward the sun and extends tail-like on the side away from the sun. The magnetosphere deflects the flow of most solar wind particles around the Earth and protects us from severe solar storms. Artist rendition of solar wind. (K. Endo / National Geophysical Data Center)." (Read more here.)

"Three objects are spinning so quickly that you only see a blur. The three objects are: a line that rotates to make a hyperboloid, a cube that rotates to make a combination of cones and hyperboloid, and three ellipses that rotate to make a cylinder. Pushing a button stops the spinning to reveal the object."

Geometric patterns on the ceilings of European cathedrals. Photos by David Stephenson.

Video by NASA simulating the evolution of the moon

Hand-cut paper sculptures by artist Jen Stark

“Prismatica consists of an arrangement of pyramid-shaped crystals affixed to an LCD screen and illuminated with programmed geometric animation. The animated patterns are precisely mapped to the vertices of the crystals, illuminating them individually and in formation. The animations are further refracted through the geometry of the crystals in accordance with the shifting perspective of the observer, which in turn alters the way the illuminations appear and interact with reflections of surrounding lights within the space.”

"Coloured smoke reveals the amazing vortex airflow patterns off the wings of airplanes."

Algorithmic Art

Fourier Transform