"Jonathan Osuch" <osuchj@avalon.net> wrote, in part:
The orbits.par file has some examples of what the new passes=o feature can do.
Indeed! Very nice, Jonathan, and thanks for including this feature. I've wanted an easy way to look at the combined set of attractor orbits for the Mandelbrot set and similar Mandeloids in Fractint for some time now, and this seems to accomplish this. If I understand its operation correctly, it iterates through all points on the screen in row major sequence, plotting the z values on each iteration. Is the orbitdelay=n feature only accessible via text insertion in the relevant .par file? I don't see it as an option on the y-screen and inserting "orbitdelay=100" in the .frm seems to have no effect. Also, when using the outside=summ or inside=0 options for rendering, is the log palette translation available? One other question: I understand that the periodicity=0 option is supposed to not plot orbits that go off the screen or bailout. Is there any way to show, of those, only the ones with a certain value of periodicity? The reason I ask this is that such would be useful in looking at the order of plotting of points in the orbit in a Julia set, which I believe is supposed to be dependent on the position of its associated bud in M-set. Now it seems to me that iterating through all the screen pixel positions is of limited usefulness without some post processing-- I'd find it more insightful to iterate over a specifically bounded area and look at where the set of orbits is. Eg. draw around one minibrot, or the main body only, or just one bud, or the buds of only one value of periodicity, and see where the set of all orbits is. If the z values were based on the scrnpix variable instead of complex plane value, zooming in wouldn't change the image ( except periodicity=0 might not be usable here-- orbits that bounce around into areas offscreen wouldn't be shown if I understand correctly). The scrnpix values could be mapped onto the bounded area of interest before feeding the resultant z or C value to the iteration part. Alternately, we could just chuck the screen position completely and get the z or C randomly within the bounded area each pixel-pass. Which I attempted in the included .par and .frm. Strangely, however, even though periodicity=0 was in effect and MOST of the diverging orbits were culled out, some points outside the bailout circle radius 2 showed up on the screen anyway. I don't understand why that would happen. Some speculation on the orbits: in Mandelbrot-like escapetime fractals we are after all looking not really at the complex plane, but rather at the behavior of sequences indexed on the C-plane. Notice on the M-set that each bud has at most a single tangent point with any other bud. It seems likely to me that all sequences within a single bud are in some sense continuous in the same way that their representations on the C-plane are, ie. if we look at all the elements of 2 sequences whose C-plane indices differ by a vanishingly small differential value, all of the corresponding elements will not differ by a finite amount-- there never is a discontinuity no matter how far the sequences are iterated. I don't know if this is true or not, but if so it seems reasonable to look for something else. Consider that in the sequence z0 -> z1 -> z2 -> ... we could just shift all elements one place to the left and truncate z0. This new sequence has to have the same attractor as the original sequence since for most purposes it IS the same sequence. We could index the first one S(1) and the second one S(2), and succeeding ones S(n) n->inf all with the same attractor. But if natural numbers are valid indices for a family of sequences, what about fractional values? Is there an S(2.5)? What is a reasonable way to define fractional iteration, IOW is there a way to extend functional iteration analogous to the way the factorial function is extended to the gamma function? And of course, what does it mean to iterate a function an imaginary or complex number of times? What do the curves that represent such families look like within the buds of the M-set, and how do they relate to objects now viewable with the passes=o option in Fractint? ---Hiram INCOMPLETE FRM FOR USING TRANSLATED PIXEL AREAS WITH passes=o: +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ MJorbitalarea_rand{ ; use with "pass=o" option, periodicity=0, orbitdelay non0. ; starting pixels chosen from user-selected areas; p1 used for M/J toggle, ; p2=(bailout,areatype(0=square,1=circle,2=ring,3=cardioid,4=cardioid ring)), ; p3=key pt, p4=scale distance(complex vals rotate), p5=secondary dist(2,4). IF( init==0 ) ; per-screen initialization ismand = 1 bailout=real(p2),type=imag(p2),keypt=p3,scale=p4,t=p5 init = 1 orbitdelay = 100 ; does this work? ENDIF IF( type==0 ) ; pixel translation pixtrans = keypt + scale*rand ; random points on([0..1],[0..1] scaled ELSE ; implement other types here pixtrans = keypt + scale*rand ; STUB:change as appropriate ENDIF IF( ismand ) ; per-pixel initialization z = 0 C = pixtrans ELSE z = pixtrans C = p1 ENDIF : z = sqr(z) + C |z| <= bailout } ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ NOT VERY INTERESTING PAR USING IT: ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ testorbitparms { ; orbitdelay cannot be set from the frm or the y-screen reset=2004 type=formula formulafile=orbit.frm formulaname=mjorbitalarea_rand ismand=y passes=o center-mag=5.78e-006/-7.005e-006/0.6666636 params=0/0/4/0/-2/-2/4/0/0/0 float=y inside=0 outside=summ logmap=yes periodicity=0 cyclerange=1/253 orbitdelay=100; colors=@grad0054.map colors=000X3r<40>v16w15x14x13y12z00<42>ze0zf0zg0zh0zi0<2>zj0yj1yj1xk1xk2\ <71>WyUWyUVzV<43>VxtVxuVxuVxvUww<23>syytyyuyy<3>zzz000000 }+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++