Tuesday, December 28, 2010
Sunday, November 21, 2010
These pictures, drawn by a harmonograph, may better be described as pictures of music. A harmonograph is a mechanical device that uses pendulums that move pen and paper simultaneously to create these images. The device was invented by a mathematician in 1844 and apparently was a popular form of entertainment at Victorian soirees.
The images vary depending on how the pendulums swing in relation to one another. Harmonic ratios used in music such as 3:2, 4:3 give the images below.
Wednesday, November 17, 2010
Tuesday, November 16, 2010
"Map the infinite checkerboard to the plane so that black squares map to squares and white squares map to quadrilaterals. Such a map is a disguised version of a discrete analytic function. This is a discrete approximation to the exponential map f(z)=e^z."
Sunday, October 24, 2010
Thursday, October 14, 2010
Sunday, October 10, 2010
Wednesday, October 6, 2010
This is probably the most important image in Chaos theory- of the Lorenz attractor. It is an illustration of what many people know as the butterfly effect- the concept that a slight change could result in a hugely different outcome.
The image corresponds to the function in three dimensions of two different variables that differ by a very small amount.
Friday, October 1, 2010
Wednesday, September 22, 2010
Each of these little critters was drawn using a very simple rule repeated over and over again (recursively). Recursion seems to pop up all over nature- whether it's coastlines that look like fractals; sea shells; or broccoli minaret. Richard Dawkins, well known for his criticism of creationism, wrote the code that generated these images. This image is printed in his book "The Blind Watchmaker" to show that as intricate and beautiful as all things in nature are, all that is required is repetition of very simple rules, weakening the intelligent design argument.
Thursday, September 16, 2010
Friday, September 10, 2010
"Visualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate the leading integer coefficient of the polynomial the number is a root of (red = 1 i.e. the algebraic integers, green = 2, blue = 3, yellow = 4...). Points becomes smaller as the other coefficients and number of terms in the polynomial become larger. View shows integers 0,1 and 2 at bottom right, +i near top."