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Dear Sam,
 
I posted a new version of QuaSZ Mac (http://www.mysticfractal.com/Programs.html) today that supports 'rfun' and 'rend'
and a 'theta' function that is compatible with Mandelbulb-type formulas.
The parser formula (Mandelbulb 8) should now work correctly, as sent.
However, you could also use:

; Mandelbulb formula by Daniel White
n=l# ; Limit box value in Formula window
rfun ; begin real values
z1=imaj(z) ; third component of z
r=sqrt(x#*x#+y#*y#+z1*z1+.0000001)
phi=n*asin(z1/r)
w=n*theta(z)
t2=cos(phi)
t1=r^n
x=t1*t2*cos(w)
y=t1*t2*sin(w)
z1=t1*sin(phi)
rend ; end real values
z=x+y*i+z1*j+c#
 
This is documented in the new QuaSZ Mac pdf help file.  Note that you change
the value in the Limit box to change the degree of the Mandelbulb.
 
Thanks for explaining a bit of what you're up to.  I'd be interested in
anything you come up with that illustrates what you call "the iterative
nature of existence", or any new variations of the Mandelbulb formula you
stumble across...
 
Cheers,
 
Terry W. Gintz
 

really cool for T.W. to do this guys cos he ain't getting much mac business! the programme is superb and terry is so responsive if you need a heads up. any way i am off to look it over!