; Date: Sun, 10 Sep 2006 17:54:46 EDT ; From: JimMuth@aol.com ; Subject: [Fractint] FOTD 11-09-06 (Elephant Trickery [6]) ; Id: <26c.e1d993e.3235e3a6@aol.com> ; --------- ; ; FOTD -- September 11, 2006 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; A bit of four-dimensional trickery is displayed in today's ; image, which tries desperately to be a Julia set of East Valley ; but never quite makes it. If the imaginary p1 parameter had ; been 90, we would have had a Julia set. As it is, we have a ; slice rotated a mere 0.2 degree toward the Elliptic direction, ; but that tiny rotation makes a world of difference. ; ; The basic outer shape of an East Valley Julia set is obvious, ; and the goofy eyes and noses are well represented, but don't ; search for elephants. None are there. They have been stretched ; out of existence, with only their infinitely stretched remains ; being visible as the vertical stripes inside the outer shell. ; ; It is curious how a rotation of only 0.2 degree can make such a ; large difference in the appearance of Julia sets, while such a ; rotation makes no difference at all in most Mandelbrot images. ; It would seem to indicate that the Mandelbrot-shaped parts of ; the Julibrot are in the form of a nest of four-dimensional hyper- ; cylinders, with the Julia direction lying parallel to the length ; of the hypercylinders. As to what such a nest of 4-D hyper- ; cylinders might look like, I have not the slightest idea. ; ; I have seen the Fractint evolver feature mentioned recently on ; the list. Yes, I do use it. It is one of the most useful ; features of the program. About one image in three is found with ; the evolver. But I usually round the evolver's parameters to ; one or two places before calculating the final image, thereby ; avoiding such awkward things as an angle of 37.7394877345823114 ; degrees, which I would enter as 37.74 degrees. BTW, today's ; image was not found with the evolver. If it had been, I might ; have let the evolver's (p1) parameters, which determine the ; angle, remain unrounded. The values are quite critical. ; ; Today's image deserves its rating of a 6. In fact a rating of ; 6-1/2 might have been a better choice. It's a relatively inter- ; esting if not particularly artistic picture. The name "Elephant ; Trickery" refers to the tricks the image plays with the Julia ; set of the central point. Changing the imag(p1) parameter to 90 ; will reveal the true Julia set, which really is a rather interes- ; ting one. ; ; The calculation time of 12 minutes is true on my tired, worn-out ; old clunker of a computer. But as long as it boots up DOS when ; I turn it on, that old warhorse will continue to be my fractal ; machine. More modern computers are far better on the internet, ; but some of them go into a panic when a DOS program is loaded. ; Those fractalists with such sensitive machines may download the ; finished GIF image of today's fractal from the FOTD web site at: ; ; ; ; A few more clouds and lower temperatures made Sunday less than ; perfect here at New Fractal Central, but the fractal cats don't ; mind the outside weather, since all they are permitted to do is ; watch it from their window. ; ; In my department, I am barely managing to keep the rush under ; control. So far it's going according to plan. I'll put the ; odds at 67 percent that the next FOTD will appear on schedule in ; 24 or so hours. Until that glorious time arrives, take care and ; check your world view for hidden errors. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Elephant_Trickery { ; time=0:12:05.35--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/0/0.9026217 params=90/89.8/2\ /0/0/0/0.27/0.00593 float=y maxiter=150000 inside=0 symmetry=none periodicity=10 colors=000AMX9NX8OW7PW6QV6RVBSYFS_JSaNScRSeVSgZTib\ UkfXmj_okf_lnKms5on6ph7qb7rY8sV9tS9qSEoQImQMkSQhTU\ fUYdWabXe`YiZXgYWfXWeWVdVVcTUbSTaRT`QS_PSZQR_RR_SR\ _SR`RfZdmarscqtdqtdqtdptepteouemuflufkufiughuggvgy\ vgxvhwvhuvhtwiswiqwipwjjwjhwjbxkaxkVxkUxkMxlIylGyl\ FymDymCymByn9zn8zn7zo5zo4zo3zo5xk7wh9udBtaDrZFqVGo\ SInPKlLMkIOiFQhBSf8Te5kMdUd7Vd8Vc9WcAWcBXbCYbDYaEZ\ aFZaG_`H_`I`_Ja_Ka_LbZMbZNcYOcYPdYReXSeXTfWUfWVgWW\ hVXhVYiUZiU_jU`jTakTblSclSdmSemRfnRgVtLTTgUShUShVS\ hVShWShWShXShXShYShYShZShZSh_Sh_Sh`Sh`ShaShaShbShb\ ShcShcShdRhdRheRheRhfRhfRhgRhgRhhRhhRhiRhiRhjRhjRh\ kRhkRhlRklRnmRqmRtnRwDLzFMzGMzIMzJMzLNzMNzNNzPNzQN\ zSOzTOzUOzWOzXPzZPz_Pz`PzbPzcQzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzYmz_mzamzcmzfmzhmzjmzlmzTmzUmzVmz\ WmzXmzXmzYmzZmz_mz`mz`mzamzbmzcmzcmzdmzemzfmzgmzgm\ zVmzRmzMmzImzEmzDmzCmzBmz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE========================================= ;