Constructing a Spiro, Cornu's spiral, Euler's spiral or Fresnel spiral

Curves are sexy. This one in particular is quite lovely because it's so simple: the further from the start of the curve (left or right from 0,0), the more it curves. If you wonder by how much it curves, hang on to your pants, here comes some math:

⎧
⎪ x(t) = a ·
t
∫
0
cos(
 π · uⁿ 
　
n
) du
⎪
⎨
⎪
⎪ y(t) = a ·
t
∫
0
sin(
 π · uⁿ 
　
n
) du
⎩

So... okay, moonwriting... what does a spiro look like? Well, that depends on the values for a, t and n. Good thing we have Processing and JavaScript, because we can simply implement the curve and observe how it changes when these values do, too!

A "spiro" curve, based on the parameters a, t and n
a: ▴ ▾
t: ▴ ▾
n: ▴ ▾

This (non-gif, non-flash, non-applet) graphic is brought to you by Processing, the visual programming language, and Processing.js, the project that brings Processing to the web, and of course me: Mike "Pomax" Kamermans. For the source code, simply click here.