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> Does anyone out there have any idea where I can get hold of an
> algorithm  that will draw a basic spiral?  Tried the search engines, but
> no luck...

You might want to try a math book, especially section on polar coordinates.

Logarithmic Spiral:
r  =  C*exp(A*theta)
where r=radius, and theta are the polar coordinates and A and C are
constants.
Try:
A=0.1, C=0.1   with 0 < theta < 15*PI/2, or
A=0.2, C=0.01 with  0 < theta < 15*PI/2


Archimedean Spiral:
r  =  A * theta^(1/M), with M <> 0  (or M != 0 for C folks).
Try:
A = 0.04, M = 1, 0 < theta < 8*PI  ("Archimedes' spiral")
A = 0.20, M = 2, 0 < theta < 8*PI ("Femat's spira")
A = 1.00, M= -1, 1.00 < theta < 6*PI ("hyperbolic spira")
A = 0.50, M= -2, 0.25 < theta < 6*PI ("litus")

Info above was from "CRC Handbook of Mathematical Curves
and Surfaces" by David H. von Seggern, CRC Press, 1990.

Of course to plot, convert (r, theta) -> (x,y) by

  x := r * cos(theta);
  y := r * sin(theta);


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