Russ Walsmith wrote:
Thanks Gerald for calling that to my attention... but I admit that I had to run about six versions of TEST { y=imag(pixel): y^2 > 1 } before I became convinced.
Shows how memory can be misleading. I was _sure_ this is documented in the online-help (it is not), but found it in my old "Fractal Creations" book (1st edition, german translation) instead: "imag() - replaces the real component by the imaginary one, sets the imaginary part to zero and by that produces a real number."
So hey, it's all good, and to quote Morgan Owens, "...the important thing here are the visual results..."
An example for this is even hardwired into Fractint as a fractal type: tim's_error.
Indeed, those and other happy outcomes are accruing to the bottom line. But if the imag(pixel) theory doesn't hang, then what is going on? I must say that the situation is way more curious than I initally supposed. There is much to ponder in this realm; e.g., I've noticed that CP8 { c1=real(pixel),c2=imag(pixel)*p3,c3=p1,c4=p2 z1=z2=z3=z4=0: t1=z1*z1-z3*z3-2*z2*z4 t2=2*z1*z2-2*z3*z4 t3=2*z1*z3+z2*z2-z4*z4 t4=2*z1*z4+2*z2*z3 z1=t1+c1,z2=t2+c2,z3=t3+p1,z4=t4+p2 z=sqrt(t1^2+t2^2+t3^2+t4^2) z < 4 } seems to be completely indifferent as to whether the value chosen for p3 is real or imaginary. Do you have any insights here?
How I would love to be able to provide a clever proof showing it _has_ to be that way :-) But why shouldn't it be possible for the fractal's cross- section for c2=real to look identical to the cross-section for c2=imag? If you rotate p3 from (1,0) only part of the way towards (0,1) the image certainly changes - try 0.707106781 for both components of p3 for a well-known fractal to appear (only in part, though). Another situation where switching p3 from (1,0) to (0,1) does change the resulting image is in having c3 and/or c4 to be non-zero (say 0.1 for example)... Regards, Gerald