Still no contact with Dr. J. He must still be sulking or celebrating the result of the FractoBowl game. Tonight, let's look at another panorama view, like last nights panorama. This time, our view point is at the very end of the filament at c=0+i. We see the filament approaching us at the bottom of the picture. Since it is actually a logarithmic spiral and we are using a logarithmic transformation, the filament is spiraling around us infinitely many times. But in the logarithmic view, this looks like a zigzag but mostly straight line. The slant is the result of the spiral angle. We can see there are 8 branches or main midgets on the filament in each complete turn of the filament. Great effect.
In the distance, we see the rest of the Mandelbrot set with the period 3 bud at the closest side. On the far side (to the right) we see the spike (c=-2).
Remember, the horizontal axis is the pan angle, sweeping around left to right through most of the horizon. The vertical corresponds to distance, up shows the furthest parts of the MSet. Along the bottom are the close up midgets and filaments.
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Figure 1. Edge-o-Rama. View from the edge of the Mandelbrot set at a filament end
Enjoy
Jay
frm:Colorit-2rPanx { ; (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=2*zc*dz+1 ; derivative, dz/dc
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.
}
MSet2-2-i-Panx { ; (c) Jay Hill, 1998 Lighting on MSet z=z^2+c
; Panorama view from end of filament at c=i
reset=1960 type=formula formulaname=colorit-2rpanx
center-mag=-4.56772/-2.67223/0.25 params=0.8/0.6/0/-1
float=y maxiter=2560 inside=0 outside=real periodicity=0
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savename=2-i-panx
}
