Motion Graphics · Science · Theory


The familiar trigonometric functions can be geometrically derived from a circle.

But what if, instead of the circle, we used a regular polygon?

In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1.

We’ll keep using the angle from the x-axis as the function’s input, instead of the distance along the shape’s boundary. (These are only the same value in the case of a unit circle!) This is why the square does not trace a straight diagonal line, as you might expect, but a segment of the tangent function. In other words, the speed of the dot around the polygon is not constant anymore, but the angle the dot makes changes at a constant rate.

Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon.


Art/Aesthetics · Bio · Design · Digital Media · Performativity · Science · Sonic/Musical · Technology · Videos


Masaki Batoh, former musician of the band Ghost and currently also an acupuncturist, recently released the album called Brain Pulse Music. Here, he experimented with his BPM Machine and used traditional Japanese ritual melodies and instrumentation to form a prayer/requiem for the victims of the Great East Japan Earthquake. Fortunately, I read some of his wise insights thanks to Co.Design

“We survivors were mentally shattered like our dead victims.” He explains to Co.Design

Batoh wanted to articulate that devastation, but the worst experiences can be tough to articulate. Talking can require that you catalog each emotion, and how do you do that when your whole psyche is a mess? How do you share the truth of what you feel, if you have no idea what that truth is?

“Human beings lie, but their brain waves never lie,” writes Batoh. And with that mantra in mind, Batoh moved beyond words. He turned to a modified EEG, what he calls a Brain Pulse Machine, to measure the brain waves of earthquake victims and play them back as music. He then mixed these tracks with his own to create Brain Pulse Music, a memorial album to raise money for Japan’s orphans.

To get Masaki Batoh’s $699.99 Brain Pulse Music Machine go to Drag City.
Hear audio samples HERE

+++ Info about the history of Brainwave Music? Read: A Young Person’s Guide to Brainwave Music: Forty years of audio from the human EEG

Electronic music pioneer Alvin Lucier amplifies his own brain waves in “Music For Solo Performer”
Nicolas Collins electronics. 1965.