Processing

I have recently gotten interested in several of the emerging simplified computing environments designed for visualization. The most prominent of these is Processing, a programming environment built around Java and designed for image and movie creation. Processing seems to be alternately billed as a content generation tool for digital artists, a visualization tool for scientists, or a learning tool for novice programmers. Right now I am just a beginner, but I have been able to knock out a few simple programs.

My sketches

Each of these was initiated in the Processing environment. For a couple of the later projects I moved things over to Eclipse.

Azulejo Graphs. Pictures of an integer lattice under various combinations of linear transformations. This was my first foray into the Processing environment. It is not very spectacular.

 

The Group of Units. This is an applet to illustrate the relationship between the elements in the group of units, U(n), up to n=50. Each colored wedge represents an element of U(n). The generators are colored red. For nongenerating elements, the darker the shade of gray, the higher the order of the element.

 

Polar Graphs. This illustrates the relationship between a polar graph and its Cartesian counterpart. Unfortunately, it only shows one example.

 

Fixed points of Mobius maps. A Mobius map is a complex map which has the form f(z)=(az+b)/(cz+d) with ad-bc≠0. The applet illustrates the flow lines and the fixed points of a Mobius map.

 

Mobius DFS. My work with a student in the fall of 2007 culminated in this applet. It illustrates the complex interplay between two Mobius transformations by plotting at the fixed points of many of the different possible compositions of those two maps. All of the information for this, including some pseudocode, comes from the (very interesting) book Indra's Pearls by Mumford and Wright.