Processing: Creative Coding and Computational Art

and began doubling. By step 80, the output had surpassed the diameter of the known universe—but
it goes way beyond that. In fact, each step from 80 to 100 is another doubling
in size—my head’s beginning to hurt, and I think you get the point.
Trigonometry
COMPUTER GRAPHICS, THE FUN, EASY WAY
The Latin word trigonometry, coined in the 16th century, was formed from three Greek
words that translate to “three-angle measure,” and simply means the study of triangles.
This is precisely what trig was used for in the second century BC, when the astronomer
Hipparchus of Rhodes created one of the first tables of trigonometry values (it was called
a table of chords back then). Unfortunately, most of Hipparchus’s work has been lost, and
we mostly know of him through the writings of others, especially Ptolemy, who based
much of his work on Hipparchus’s earlier work. Ptolemy, you may remember, is the guy
who said that Earth was at the center of the universe, which was eventually refuted by
Copernicus 1,400 years later. Hipparchus apparently used his chord tables to help him predict
things like eclipses, star positions, distance to the moon, and the length of a year,
which he predicted to within 6.5 minutes. I think it’s time we give Hipparchus his due.
Hipparchus’s reputation aside, solving for angles and sides of triangles is not terribly inspiring,
and precisely what contributed to my dazed stare out the classroom window when I
first studied it. Since ancient times (even before I was in junior high school), trig has
emerged as a fundamental tool in many fields, from astronomy to architecture to engineering
to 3D gaming, and yes, also to code art. Trig is much more than the study of triangles;
it figures significantly in the study of waves, impacting our understanding of sound,
radio, and light, among other physical phenomena.
Trigonometry is also really simple. I know this may sound odd, but aside from having to
learn a couple scary Greek symbols and basic theory, trig is really just an extension of the
Pythagorean theorem (at least the part of trig you’ll need). Although some basic theory is
helpful to begin to grasp the full power of trigonometry, it is possible to begin playing with
the trig functions almost immediately, learning experientially as you experiment with
them. The trig functions that you’ll mostly use are sine, cosine, and tangent. There are a
few others you’ll look at later on in the book, but an amazing amount of stuff can be done
with just these three.
I like to think of the trig functions almost as dabs of paint on my palette. I begin playing
with the trig dabs, inserting different values here and there, and watching what happens.
Sometimes I end up with really long and convoluted expressions, completely outside of my
understanding, that make engaging, beautiful images or animations; other times I get a
garbled mess. Part of the fun is in not exactly knowing what you’re going to get.
Fortunately, as an artist, I can get away with this aesthetically driven, semi-clueless
approach to trig. I also can’t help wondering, had math been taught this way when I was in
school, perhaps I would have enjoyed math class more and done less window gazing.
Interestingly, as I’ve gotten older, I’ve found the more I play with stuff like trig, the more
interested I get in understanding the underlying theory. I also think this aesthetic approach
to learning math increases retention, especially for artists.
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