🚀 go-pugleaf

In article <1dro9cINN8rb@agate.berkeley.edu> shirriff@sprite.berkeley.edu (Ken Shirriff) writes:
>In article <1992Nov11.182309.8811@mnemosyne.cs.du.edu> mccasal@nyx.cs.du.edu (Massimo Casal) writes:
>>when must i stop the iteration when i calculate the julia set of c*e^z?
>>when the real part is > value?or when the modulus is >value?
>
>The stopping limit for c*e^z is problematic, since an extremely large value
>of z can get mapped back to something small.  The second problem is that
>your floating point can overflow very quickly.  The usual stopping point is
>real part > large value (note: not abs(real part)), since this implies the next
>iteration will be extremely large.  The disadvantage is that you will stop
>for some large values where you shouldn't.  The visual appearance is that
>the many thin petals will suddenly clump together into one thick petal, when
>they should remain as thin petals.

But apparently there is justification for this algorithm.  See

   Marilyn B. Durkin.  The accuracy of computer algorithms in
   dynamical systems.  _International J. of Bifurcation and Chaos_
   1(3), 1991.

for details.  Or you might want to contact Lynne directly at
lynne@math.bu.edu.

-- 
Tom Scavo
scavo@cie.uoregon.edu