FOTD -- July 25, 2009 (No Rating) Fractal visionaries and enthusiasts: Friday turned unexpectedly busy here at Fractal Central, leaving almost no time for a proper fractal, much less a new type of fractal. What we have is an almost-Julia set with a bridge across its center. This bridge is a side view of the north branch of the valley leading to the period-4 bud on the north- east shore line of the main bay of the Mandelbrot set. The wedge-shaped valley has become a stripe with parallel sides because, regardless of where the Z-points are initialized in the Mandelbrot set, they eventually settle into the same orbits. I have no time for the technical details so just take my word for it. The image is a harmless one -- a Julia outline with a blue stripe running diagonally across the center. The area north and east of the stripe has many spirals, all spiralling clockwise, while the area south and west has only vague hints of spirals, and these are spiralling counter-clockwise. Checking the orbits will show that the northeast half of the area inside the Julia outline lies inside the period-4 bud; the southwest half lies on the outside. Some of the orbits are quite interesting. I leave it to the individual fractalist to find these orbits. I named the image "Northeast Bride". I had intended to type the word 'bridge' but typed 'bride' instead. I kind of liked the error, so I decided to let it remain. As for a rating, forget it. How many who have remained with the list all these years are really thrilled by seeing such trite images? At least the calculation time is reasonable. Who can complain about a calculation time of under 2-1/2 minutes? And if there are any who do complain, relief may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is or soon will be posted. Hazy sun but otherwise pleasant weather prevailed here at Fractal Central on Friday. An afternoon threat of rain proved to be a false alarm. The fractal cats approved of the dryness and temperature of 82F 28C. My day was very busy, even with FL helping. There is a 50- percent chance that the next FOTD will be posted in 24 hours. The other 50 percent is that we decide to take the day off. Until whenever, take care, and something very important is happening unseen just beneath the surface. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Northeast_Bride { ; time=0:02:26.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t center-mag=-0.00921296/0.0053159/1.11/1/-105/0 params=90/90/92/89/0.241/0.512/0/0 float=y maxiter=25000 inside=0 logmap=-3 periodicity=10 colors=000UV9UVCUWEUWGVWIWWLWWNXXPYXRYXUZXW_XY_X_`\ VY`UXaSWaRVaPUbOTbMScLRcJQcIPdGOdFNdHMgIJiKHkMFmOD\ pQBrS9bazbazbazbazbbzbbzbbzbczbczbczbdzbdzbdzbdzbe\ zbezbezafzafzafzagzagzagzahzahzahzahzaizaizaizajza\ jzajzakzakzakzakzalzalzalzamzamzamzanzanzanzaozaoz\ aozaoz`pz`pz`pz`qz`qz`qz`rz`rz`rz`rz`sz`sz`sz`tz`t\ z`tz`uz`uz`uz`vz`vz`vz`vz`wz`wz`wz`xz`xz`xz`yzayzb\ yzczzdzzezzfzzgzzhzzizzjzzkzzlzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzznzzozzpzzqz\ zrzzszztzzuzzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================