Hello,

I was in the book store tonight paging through Curtis Rhoades' (sp?) book
on Computer Music and noticed a page with a picture of a surface being
traced by an orbit.  I've had a small collection of complex 3D surfaces of
the form Z(x,y) which I wasn't sure how best to use to generate sounds.  In
the past I had just rastored through them snaking back and forth.  Using
orbit opens up a large number of possibilities.  For example a circular
orbit could trace along the surface and the Z(x(t), y(t)) is taken as the
amplitude.  Modulations could be applied to the circle center point,
circle->ellipse.  Instead of circular orbits chaotic oscillators could
define the X, Y coordinates although these would not be tuned.

I think something like the following will work:

y=sin(t)
x=cos(t)

Z(x, y)=sin^2*(sqrt(x^2+y^2))
Z(x, y)=ln(x^2+y^2)
Z(x, y)=x-1/12*x^3-1/4*y^2+1/2
Z(x, y)=-5*x/(x^2+y^2+1)
Z(x, y)=1/3*x^3-x*y^2
etc...

These equations are from Clifford Pickover's "Computers and the Imagination"
Start oscil can be used to generate sine and cosine.  Then modulate by
varying radius, center etc.  This opens up a large class of synthesis...

Bye,
Hans Mikelson