Tonight's fractal is a reply to a post by Tim Wegner. It comes straight from Dr. J reading his email while waiting for the big game Fractobowl. Only in fractal land can we get a view like this one, one of his private collection of test photos of the latest in Fracto-fish-bowls. The fish must be sleeping or may not have been introduced into the bowl yet.
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> From: Tim Wegner <twegner@phoenix.net>
> You can probably get all the flexibility you are asking for by using
formula parsers. In Fractint's lingo, just transform Pixel before you use
it. [...] Perhaps some of our more mathematically inclined artists
might take up the challenge and upload an example of what I am talking about.
Dr. J suggestion is included here:
Try this as an example, something like
1) c = exp(flip(pixel))-p1
gives me a panorama view of your fractal from the point p1. If the fractal is the MSet, and p1=1.75, we get a panorama view from a central point in the period 3 cardioid at -1.75. See Figure 1. Azimuth is horizontal, range is up. The spike and the main cardioid are both visible. Parameter files another images is included below (Figure 2). In this one we see Dr. experimented with flowing water fish bowls. Rumor has it that no fish survive long in these bowls.
Dr. J enjoyed the game immensely, and sent in the compressed image of a panorama view of the FractoBowl. This picture, Figure 3, taken from above (in some dimension) the city shows the fans leaving is several streams. Equation 1 can be applied as a panorama function to most any fractal, much lick a fisheye lens.
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Figure 1. FractoFishBowl
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Figure 2. FractoFishBowl, Flowing Water
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Figure 3. FractoBowl, Panorama View
You can get your 3D glasses, two sets, along with 27 striking astronomical images in the March 1998 issue of Astronomy magazine. So aim your Car-dioid toward your nearest magazine rack. Future FotN pictures may be in 3D.
Enjoy your FractoBowl Game. Dr. J must have gotten a good seat!
Jay
frm:PanoramaMandelbrot { ; Panorama Mandelbrot set
z = 0, c = exp(flip(pixel))-p2:
z = z*z + c
|z| < 4
}
Panorama_3Cardioid { ; (c) Jay Hill, 1998
; Panorama view from a central point in the period 3
; cardioid at -1.75. Azimuth is horizontal, range is up.
; The spike and the main cardioid are both visible.
reset=1960 type=formula formulafile=color102.par
formulaname=panoramamandelbrot
center-mag=-2.66454e-015/-2.00267/0.295858 params=0/0/1.76354/0
float=y maxiter=256 inside=0 outside=summ periodicity=0
colors=000<7>00z<6>ccc<8>w0w<6>hhh<8\
>z00<6>mmm<2>qg`seWtcRvaMw_IyYDzW8<6\
>jjj<8>zz0<6>mmm<8>0w0<6>mmm<8>0zz<6\
>rrr<56>00z00z00y<81>001000000000
savename=Pan3card
}
Panorama_4Cardioid { ; (c) Jay Hill, 1998
; Panorama view from a central point in the period 4
; cardioid at -.16+i. Azimuth is horizontal, range is up.
; The filament and the main cardioid are both visible.
reset=1960 type=formula formulafile=color102.par
formulaname=panoramamandelbrot
center-mag=0.612193/-2.57748/0.2583549
params=0/0/0.15967/-1.03437 float=y
maxiter=256 inside=0 outside=summ periodicity=0
colors=000<7>00z<6>ccc<8>UwA<6>hhh<8\
>z00<6>mmm<2>qg`seWtcRvaMw_IyYDzW8<6\
>jjj<8>zz0<6>mmm<8>0w0<6>mmm<8>0zz<6\
>rrr<56>00z00z00y<81>001000000000
savename=Pan4car2
}
frm:Colorit-3rPan { ; (c) Jay Hill, 1998
; p1= light angle (cos a, sin a)
; p2 = pan view point
if(p1==0)
p1=1
endif
done = 1, iter=0, z = 0, zc = 0, dz=1,
c = exp(flip(pixel))-p2
: ; initialization.
iter = iter+1 ; gotta count em
dz=3*sqr(zc)*dz+1 ; derivative, dz/dc
zc=zc*sqr(zc) + c ; standard MSet iteration
if(|zc| >= 1024) ; Bailout
z = z -8 + ((sin(2*pi*iter/256)*Real(p1*dz/zc))>0) + iter
done=-1 ; Set flag to force an exit.
endif
done >= 0 ; Continue if the flag >=0.
}
FractoBowlPan { ; (c) Jay Hill, 1998 Lighting on 3-MSet
; Panorama view of FractoBowl
reset=1960 type=formula formulaname=colorit-3rpan
center-mag=3.68212/-4.36448/0.724696
params=0.8/0.6/0.2755/-0.98776
float=y maxiter=2560 inside=0
outside=real periodicity=0
colors=UmAVTSxusVTTxvtVTTxvuUUUwwwKK\
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savename=panobowl
}
