Ornamental Orbits

October 29, 2012

As they say, "A picture is worth a thousand words," so scientific papers contain many graphs and other images. Computationally speaking, there are about 100,000 24-bit words in a multi-megapixel photograph, so this adage needs to be updated.

Programmers use whatever devices are available to them to produce graphic images. The oscilloscope was likely the first such apparatus for producing graphical output from computers, followed by pen plotters and printers. The pen plotters could produce simple images using vector graphics, and printers could produce ASCII art images, such as the figure, below.

The Lenna image, rendered as ASCII art. Aliasing appears when the image is shrunk to such a small size, since the characters are separated in regular rows and columns. (Click for larger image without aliasing)

The first graphics I did on a computer was printing computed phase diagrams for binary alloys. This was done in the APL programming language, and the diagrams were rendered as huge matrices in which the numbers were replaced by keyboard characters. Very nicely, the APL character set has many Greek characters, which were convenient for labeling alpha phases, etc.

When I finally had a vector graphics terminal in my office, I played with a common program at the time that gave a graphic based on a person's name. The program was extremely simple, just plotting lines between (x,y) points defined in a phase space of characters. The points were defined as (a_i,a_i+1), where a_i is the ordinal value of the character (a=1, b=2, etc.). This is easy to do with a spreadsheet program, as the following example demonstrates.

"George Washington" rendered in alphabetic phase space. The points are (ai,ai+1), where ai is the ordinal value of the character. Graph rendered using Gnumeric.

Often, scientific calculations result in aesthetically pleasing images. The reason for this might be that our eyes are drawn to symmetrical vistas, and symmetry abounds in the equations that describe most physical processes. To investigate the possibility of generating "art" from a very basic physical process, I wrote a program (source code available, here) to display the trajectory of an object under the influence of a basic inverse square (1/r²) force from a random set of ten other objects in a plane.

This is like the gravitational attraction experienced by a strange asteroid entering a strange planetary system. The asteroid is strange, since it's initially at rest, and the planetary system is strange because there is no star, all the planets have the same mass, and a planet will disappear when it appears that the asteroid will impact. This last condition allows the asteroid to enter a somewhat stable orbit, since all the disastrous (pun intended) paths have been removed.

This disappearing planet case is reminiscent of the episode, "Collision Course," of the television series, Space: 1999.[1] The story line of that series is that the far side of the Moon was used as a dumping ground for Earth's nuclear waste, and the waste erupts into an explosion that pulls the Moon, with several hundred people living there, out of its orbit and into deep space.

This series was unlike other space adventure series, since the scripts often had a surreal character. The "Collision Course" episode revolved around the idea that the Moon was on course to collide with an alien planet, Atheria. As foretold by the Queen of Atheria, the planet disappeared at the point of collision. I must admit that since I'm a fan of "hard" science fiction, I never enjoy this type of story.

The following is a gallery of obits from my program, chosen for their aesthetic value. You can rerun these, perhaps with minor modification of the positions to see what happens; or, modify the program to give different results. Since this is "art," any physics errors you may find in the source code were strictly intentional (LOL).

A gallery of some calculated orbits. Click images to see positions of the ten random objects in the plane. The test object starts at (0,0)

Reference:

1. Space:1999 page on the Internet Movie Database.