In article <MPG.14a492244e6b256098985c@news.povray.org>, 
jam### [at] dh70qdu-netcom (Jamie Davison) wrote:

> I looked at the source, and whimpered...
> 
> Too much mathematics <shudder>

It's not that hard...it's a pretty simple function, made of even simpler 
pieces.

The full equation is:
1/(sqr(x)+sqr(z)+0.3) + sin(atan2(x,z)*7 + y*10)*0.025 = 0

The 1/(sqr(x)+sqr(z)+0.3) part is what gives it it's shape...it is based 
on 1/R where R is the distance from the y axis. The equation for R is 
sqrt(sqr(x) + sqr(z)), so that is just 1/(sqr(R)+0.3). The "+ 0.3" part 
keeps it from going to 1/0 at the y axis, and limits the depth of the 
vortex (Since the square of distance from the axis can't be negative, it 
can't go further than 1/0.3. I just got this value by trial and error.). 
You can graph the function 1/(sqr(x)+0.3) in any graphing program to get 
a cross-section of the basic vortex.

The second half adds the ripples:
sin(atan2(x,z)*7 + y*10)*0.025
The value of atan2(x,z) is simply the angle around the y axis measured 
in radians, similar to the "radial" pattern. I multiplied that by 7 to 
get more ripples, giving it a higher frequency, and then added an amount 
depending on height to make it spiral in as the sides of the vortex got 
steeper (basically rotating the density field by a height-dependant 
amount. Since the height changes more rapidly in the "walls" of the 
vortex, it will spiral in tighter.).
I took the sin() of this value to get the waves and added the result to 
the basic vortex shape...the sin() function produces a nice, smooth 
periodic waveform which makes it useful for this sort of thing. The 
*0.025 part scales the size of the ripples down, so they barely make an 
impression on the surface.

So most of it was just piecing together simple little expressions...

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

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