A few days ago I asked if anyone on this forum was familiar with the phenomenon whereby a Mandeloid, even when done as a union of the sets produced from all its critical points, ends up showing straight or smoothly curved lines on the boundary between inside and outside points, or else in the outside iteration zones in a discontinuous way (eg. smoothly sided polygons of iter=7 bordering a region with iter=15). I didn't get any answers on this, as to whether this is a genuine effect or not-- one doesn't see this in the classic M-set, nor as far as I have been able to tell in Mandeloids of integer power, but on encountering it once more and unintentionally, I am more confident that it is a genuine effect. Today though I came across an example of this phenomenon (accidentally) that was so thorough that the smooth lines actually extend on down fractally-- infinitely more such regions as the scale gets smaller. A couple of days ago Jim M. mentioned a Mandeloid using exponents 0.15 and -0.15, commenting that all the points were inside points (ie. there was no attraction to infinity to generate an outside). It got me thinking about the possibility of having the attractor for outside points being something other than infinity for fractals like this where the generator itself can't possibly go to infinity. So, on the way to writing a .frm that could display many orbits of outside points, I needed a sentry value to put in one of the parameters to indicate it was an orbit fractal and not the usual bailout kind; the number e came to mind since it would not likely be hit accidentally during the nonorbit iteration. I accidentally put this in the place for the exponent of the Mandeloid instead-- being a good approximation for an irrational number, an interesting thing happened on the _non_ orbit screen: the fractal generated had the "fault lines" all over one side of the fractal. Zooming in, they become so numerous in some areas that they become the dominant visual theme. One particular area is very reminiscent of the Sierpinski triangle-- with the triangles slightly rearranged and etched away, but trailing down into the infinitesimal (while blue-shifting as they get smaller). It can be generated by this .frm-.par pair: Sincerely, Hiram =================PAR BEGIN===================== SierpinskiUnwoven { ; The fault lines from fractional order Mandeloid powers ; proliferate @ exp=e. The torn triangles in fractal dimen ; sion remind me of the Sierpinski triangle with its parts ; distorted rearranged and partially covered. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=orbit_mandeloid passes=1 center-mag=-0.65861073150000000/+0.17502501600000000/86.33309/1/-47.5590\ 028298907441/0.159744895096057493 params=2.71828182845905/0/2.71828182845905/0/4/0 float=y maxiter=10000 inside=0; colors=@spectrm3.map colors=000oC8<7>uM4vO3vP3<2>yT1zV0zY0<3>xj0xm0wp0ws0vw1<3>hxHdxL`xPXyU<1\ 6>WyoWypWyq<2>WyuVzwWww<3>cgwdcwf_whWwjSw<4>e8wd4wc0w<9>Y0kY0jX0h<2>V0eU\ 0cU0c<118>TQTTQTTRT<3>SSS000000zzzc00<6>n00o00p00<3>w00<7>nE9mGAlIB<3>fP\ GeRHdTI<9>xU2 } ==================END PAR======================= ==================BEGIN FRM===================== Orbit_Mandeloid{ ; p1=A in z->z^A+C,p2=(sentry to do orbit,radius), ; p3=(bailout for nonorbit,angle subdivisions for orbit) IF(isinit==0) isinit = 1 A = p1 lim = real(p3), anglediv = trunc(imag(p3)), angle = 2*pi / anglediv sentry = real(p2), radius = imag(p2) rotfactor = cos(angle) + flip(sin(angle)) orbititer = trunc( (maxit - 1) / anglediv ) ENDIF isorbit = ( real(pixel) == sentry ) IF(isorbit) C_ct = 0 ; count C values on the radius i_ct = 0 ; count iterations per C value C = radius ; set initial C position to radius along +real axis continue = 1 ; the "do not bail out" flag ELSE C = pixel ENDIF z = 0 ; in either case z starts at 0 : IF(isorbit) IF(C_ct >= anglediv) ; should terminate continue = 0 ELSE ; normal iteration for orbit screen z = z^A + C i_ct = i_ct + 1 IF(i_ct >= orbititer) ; go to the next C value C_ct = C_ct + 1, i_ct = 0 z = 0 C = C * rotfactor ; rotate C-value around the circle ENDIF ENDIF ELSE z = z^A + C continue = ( |z| <= lim ) ENDIF continue } =================END FRM=========================