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After the blast the other night and again last night, Dr. J is not feeling so good. While recuperating, he is looking over some plans for a new laboratory. This one promises to be slightly more complicated and hopefully more blast resistant than the last one. You who have been reading these posts know about Dr. J's ex-laboratory, and what he called experiments. These are buds and filaments lined in long rows which seem to stretch off into infinity. His new lab will also have experiments lining both sides or is it top and bottom. It really confuses Dr. J when I try to clarify that question. He just gets disgusted with us 3D people. He lives in a many dimensional space, you see. Oh never mind, where was I. Oh yes. He Fracto-Faxed me part of the plans for the new wing (he may still try to refurbish the other one).
Oh, I need to update you on Dr. J. Dr. J is NOT fine, being slightly more than a little surprised (as reported after the last time) by the explosion which took off most of his lab roof and sent him tumbling. Shock has worn off and is replaced by the usual pains and sticker shock (for the repairs). He still grumbles more about the repair costs.
In Figure 1, I show, turned on its side, some of the new wing. It promises to be a very nice place to explore many interesting 'experiments'. Even better, Dr. J claims there are more bent midgets here too.
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Figure 1. The new wing of Dr. J's Laboratory.
A little math. The formula uses the exp function to flatten out the cardioid boundary of the Mandelbrot set. The buds are placed in a line, the spacing is according to the interior angle. Then an inverse (1/x) function centered on the base of the period three bud turn the whole thing inside out. The little details so hard to see in close to the 3 bud base are expanded and moved far out from the origin. The original MSet is folded in to a small part near the origin. Finally, exact tests are used to allow skipping expensive iterations in period 1, 2, and 3 components.
Stay healthy,
Jay
frm:Stretch3 { ; Flattened cardioid by Jay R. Hill, 1998
; Classic Mandelbrot set fractal, transformed
; use: maxiter=256 inside=249 outside=summ symmetry=xaxis periodicity=0
p = 0.5*exp(Pixel), c=p*(1-p), z = 0, done = 1, zc = 0
s=|c|, t1=(256*s - 96)*s + 32*Real(c); period 1 cardioid test
t2=16*s + 32*Real(c) + 16 ; period 2 circle test
B=sqrt(-4*c-7), t3=|8+4*c*(1-B)|, t4=|8+4*c*(1+B)| ; period 3 components
test
z=z + 249*(t1<=3) + 250*(t2<=1) + 251*(t3<=1) + 252*(t4<=1) ;
set colors
if(z>0) ; periods 1, 2 and 3 have z>0.
done=-1 ; color is set for c in a known component, skip iterations
endif
: ; initialization.
zc=sqr(zc) + c ; standard MSet iteration
if (|zc| >= 4) ; Bailout at 4
done=-1 ; Set flag to force an exit.
endif
done >= 0 ; Continue if the flag >=0.
}
Stretch3-i00 { ; (C) Jay Hill, 1998
; invert on (0,-2*pi/3)
reset=1960 type=formula formulafile=stretch.par formulaname=stretch3
center-mag=2.6999/0/0.3333333/1/-90 float=y maxiter=3000 inside=0
outside=summ invert=1/0/-2.094395102393 periodicity=0
colors=mKAmmm<5>PP4<7>wwB<15>00N<46>00v00w00w00w<78>0UU1UU1UV<76>mmw<9>5\
55m44wwm3cUmmm111000
}
Stretch3-i08 { ; (C) Jay Hill, 1998
; invert on (0,-2*pi/3)
reset=1960 type=formula formulafile=stretch.par formulaname=stretch3
center-mag=2.6999/8/0.3333333/1/-90 float=y maxiter=3000 inside=0
outside=summ invert=1/0/-2.094395102393 periodicity=0
colors=mKA000<13>wwB<15>00N<46>00v00w00w00w<78>0UU1UU1UV<76>mmw<9>555m44\
wwm3cUmmm111000
}
Stretch3-i16 { ; (C) Jay Hill, 1998
; invert on (0,-2*pi/3)
reset=1960 type=formula formulafile=stretch.par formulaname=stretch3
center-mag=2.6999/16/0.3333333/1/-90 float=y maxiter=6000 inside=0
outside=summ invert=1/0/-2.094395102393 periodicity=0
colors=mKA000<13>wwB<15>00N<46>00v00w00w00w<78>0UU1UU1UV<76>mmw<9>555m44\
wwm3cUmmm111000
}
Stretch3-i24 { ; (C) Jay Hill, 1998
; invert on (0,-2*pi/3)
reset=1960 type=formula formulafile=stretch.par formulaname=stretch3
center-mag=2.6999/24/0.3333333/1/-90 float=y maxiter=9000 inside=0
outside=summ invert=1/0/-2.094395102393 periodicity=0
colors=mKA000<13>wwB<15>00N<46>00v00w00w00w<78>0UU1UU1UV<76>mmw<9>555m44\
wwm3cUmmm111000
}
Stretch3-i32 { ; (C) Jay Hill, 1998
; invert on (0,-2*pi/3)
reset=1960 type=formula formulafile=stretch.par formulaname=stretch3
center-mag=2.6999/32/0.3333333/1/-90 float=y maxiter=12000 inside=0
outside=summ invert=1/0/-2.094395102393 periodicity=0
colors=mKA000<13>wwB<15>00N<46>00v00w00w00w<78>0UU1UU1UV<76>mmw<9>555m44\
wwm3cUmmm111000
}
Stretch3-i40 { ; (C) Jay Hill, 1998
; invert on (0,-2*pi/3)
reset=1960 type=formula formulafile=stretch.par formulaname=stretch3
center-mag=2.6999/40/0.3333333/1/-90 float=y maxiter=16000 inside=0
outside=summ invert=1/0/-2.094395102393 periodicity=0
colors=mKA000<13>wwB<15>00N<46>00v00w00w00w<78>0UU1UU1UV<76>mmw<9>555m44\
wwm3cUmmm111000
}
