FOTD -- March 20, 2008 (Rating 7) Fractal visionaries and enthusiasts: I often see TV shows about true-believing psychics who know that psychic powers do exist, and I see TV shows about true-disbelie- ving skeptics who know that such powers are not real, and both sides are adamant in their opposing convictions. My opinion is that both sides are correct. Psychic powers are not real but they do exist. (Don't ask for an explanation, just add this paradox to the long list of other paradoxes uncovered by our old friend, 'modern science'.) The dispute is as silly and meaning- less as debating whether fractals exist. Fractals are not real, but they do exist -- just like ghosts and bigfoots. Take today's fractal image for example. Run the included para- meter file and a minute later you will see the image on your screen. There is no doubt of it, fractals do exist, for you can see one with your own eyes, and what you see most certainly does not exist only in your mind (whatever that means). But now try to find the physical object that was photographed to produce the image on the screen. No matter where or how far you search, you will never find the actual physical object. No such object exists. When we imply the fullest meaning of the word 'real', fractals do not quite measure up. Today's image lies in the parent fractal that comes about when various portions of Z^3 and Z^5 are combined and 1.038i is added to initial Z. I think this is the first time I have used the ability of the MandAutoCritInZ formula to vary the automatically preset value of initial Z. The result appears a lot more like a critical fractal than the one the formula calculates automati- cally when imag(p4) is left at zero. But the resulting fractal is not exactly critical. Today's image shows a 'dry valley', which is a sure sign that a fractal is not exactly critical. To add interest I rendered the image with the outside set to 'tdis' and the inside set to 'fmod'. The result reminds me of vaguely threatening terraces, so I named the image "Darkest Terraces". The calculation time of 1-2/3 minutes will pass like lightning for the true fractal fan. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image will also pass like lightning. With a temperature of 48F 9C, it was not too chilly here at F.C. on Wednesday, but thick clouds, fog, and near continuous showers kept it far from being pleasant. The fractal DSH cats agreed, and spent the day sleeping on the couch. My day was uneventful; the work was finished by 3pm. If the next 24 hours are just as uneventful, the FOTD for March 21 will appear at the end of that period. Until then, take care, and where was the Mandelbrot set 100 years ago? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Darkest_Terraces { ; time=0:01:38.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.002723103650706/+1.392157872857252/\ 91400.53/1/62.5/0 params=1.3/3/0.67/5/0/0/0/1.038 float=y maxiter=1500 inside=fmod proximity=0.001 outside=tdis logmap=yes periodicity=10 colors=000REibGgaHe_IcZKaXL_WNYUPWTSURUSRWSQYSQWTP\ VTPUTPSRQQPQOORMMRLKRKJQIHPHFNEEMCCK9AK79MCAOJAQMA\ OPBOSBQVBSZCUcCWhCYlCXiBXgBXeAXcAWaAW_9WX9WV9WT8VR\ 8VP7VN7VK7VI6UG6UE6UC5UA5U85S98QABOBEMCHKDKIENGFQE\ GTDGVEFTFFSFFRGEQHEPHEOIENJDMJDLKDKLDJLCHMCGNCFNCE\ OBDPBCPBBQBARA9RA8SA7SA6TB6TC6TD6TE6TF6TG6TG6TH6TI\ 6TJ6TK6TL6TM6TM69okBpiCpgEpfFpdGpcIpaJp`KpZMpYNpWO\ pVQpTRpSSpQUpPVpNWpMYpKZpJ_pHapGbpEcpD4_65a76b77c7\ 7d88f89g89h9Ai9Bk9Bl9CmADnAEpAEqBFrBGsBGuCHvCIwCIx\ CKwDLwEMwFOwGPwHQwHRwITwJUwKVwLXvLYvMZvN_vOavPbvPc\ vQevRfvSgvThvTfsUeqVdoWclWbjXahY`fY_cZZb_Ya_X``V_a\ U_bTZbSZeR_jQ_oP_tO`xNazMazLazKazJazJazIazIavIarHa\ mHahH`cG_cGZbFYbFXaFWaEW`EW`EW_DW_DXZDYZDX_DW_DV_D\ U_DT_DS_DS_DR`DQ`DP`DO`DN`DM`DM`ER_EV_EZ_FcZFgZFkZ\ GgWGdUG`SGYQGUNGRLGNJGKHGHFJKGMNHOPHRSITVIWXJY_J`b\ KcdLegLhjMjlMmoNoqNjoRemV } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================