Fractal visionaries:

When I saw the first fractals that contained complex or imaginary exponents of Z in their formula, I was disappointed.  The pictures on my screen were split along the negative X-axis.  They looked like part of the fractal was missing.  I soon found out that this was indeed the case.  Due to the multi-valued nature of the complex log functions, such fractals are infinite, and cannot be displayed in their entirety.  But enough can be displayed to reveal that they spiral endlessly around the origin in a screw motion.

This inability to display the entire fractal was a situation that needed to be corrected, so I started experimenting.  I soon noticed that changing the sign of the exponent causes a fractal to change the direction of its spiral.  What would happen, I wondered, if a formula something like (z^x)+(z^(-x)) or (z^x)^(-x) were iterated with x being complex or imaginary.  Would the opposite spirals cancel out, leaving a fractal with complex or imaginary features, but without the annoying X-axis discontinuity?  I wrote a few test formulas, and the answer was yes, in some cases the opposite spirals did cancel out, leaving some very interesting one-piece complex and imaginary fractals.

Today's fractal, Cyclone, is drawn from one of those test formulas.  I've added a few frills to the formula to make it more interesting, but it's still basically the same idea.  Instead of spiraling off the screen into imaginary planes, the fractal spirals endlessly into the origin.  I haven't followed the spiral very deep, but it appears to show ever-changing features as one goes deeper.

The picture itself is immediately striking -- the way I like a fractal to be -- with a brilliant red background blazing through mysterious foreground shapes.  The finished image has been posted, of course, to a.b.p.f. and a.f.p.

Jim Muth
jamth@mindspring.com


START COMBINED FILE FOR 19.6===============================

Into_the_Eye       { ; time=0:00:04.99-SF5 on P4-2000
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  inside=bof60 logmap=yes symmetry=none periodicity=9
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frm:Mytest07  {; Jim Muth
z=pixel, a=real(p2), b=imag(p2), c=b*(pixel):
z=(((z^p1)*(z+a))^p3)^(-p3)+c,
|z|<=100
}

END COMBINED FILE==========================================