; Date: Sat, 16 Aug 2008 22:26:32 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 17-08-08 (It Is Impossible [6.5]) ; ; Id: <1.5.4.16.20080816222720.2abfcc2e@pop.mindspring.com> ; --------- ; ; FOTD -- August 17, 2008 (Rating 6.5) ; ; Fractal visionaries and enthusiasts: ; ; As the title of today's image implies, the image is impossible. ; With the value of real(p5) set to -2, the minibrots deep in the ; parent fractal must be of the order -2. Minibrots of a negative ; order are by definition impossible however. If they did exist, ; they would have a number of lobes 1 less that their order, but ; how can a minibrot have minus-3 lobes? ; ; This is what I decided to find out in the search for today's ; fractal, when I set the value of real(p5) at minus-2. The first ; problem was that, with such a large escape radius and a negative ; exponent of Z, the image turned out to be all blank inside stuff ; -- an evaporated image. This problem was quickly solved by re- ; rendering the blank screen with an active inside fill. In this ; case I first tried the 'bof61' fill. ; ; When I did this, a ghostly arrowhead-shaped thing appeared, only ; vaguely resembling a Mandelbrot shape with a rudimentary East ; Valley. A closer search of this proto-East Valley revealed the ; symmetries that indicate minibrots are at the center. Zooming ; in on a prominent symmetry, I found today's scene, with its ; pseudo-minibrot at the center. The 'bof61' inside fill revealed ; the scene, but I found that the 'fmod' fill actually works best ; with this image. ; ; And what does a minibrot with minus-3 lobes look like? That ; question can be answered by checking today's image. I'm not ; sure that the thing at the center is a minibrot at all, but with ; its symmetrical surroundings, it sure does seem to be trying to ; be one. ; ; After all this mathematical excitement, I could rate the image ; no higher than a 6.5, 1/2 point of which is due to my coloring. ; ; The calculation time of a fireball 45 seconds will burn no one. ; And as always, the finished image is or soon will be available ; on the FOTD web site at: ; ; ; ; A perfect day here at Fractal Central on Saturday pleased humans ; and cats alike. The warm sun, blue sky and temperature of 77F ; 25C were perfect for everything but skiing. I doubt that anyone ; in the area had planned on skiing however. ; ; The day's FOTD might be a bit hasty, but the next FOTD is due in ; 24 hours. I suspect it will actually be ready on time, and it ; might even be a pretty good one. Until then, take care and make ; the impossible possible. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= It_Is_Impossible { ; time=0:00:45.13-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 periodicity=10 center-mag=+0.21857780829516740/+0.051382415163788\ 77/284576.4/1/-87.5/0 params=0/0/0/0/0/0/0/0/-2/0.5 float=y maxiter=1000 inside=fmod proximity=0.051 colors=000gaEhcEjeElgDniDokDjdLfZSaTZYMeTGlPAsrmmX\ Cn`DldDihEglFepFbtG`xHZzHXzKVyNUwPSccctVPsXOq_MpaL\ qbNrbPsbRtbTubVvcWwcYxc_UUPzcczddzdfzdhzdjzdlzdmze\ kzfjxfiughsggqhfoielicjjbhjafk`cl_alZ_mYYmX`kWciVf\ gUuuMppPlkRhfTdbV`YXXT_TPaPKcLFeF9eHBgIDhJFjKHkLJl\ MLnNNoOPpPRrQTsLXvOWuRVtUUtXTs_SsbRreQqhPqkOpnNpqM\ oPTGdPYsLooMlkMjgMgcNe_NcXN`TNZPOXLOUHOSBMOEOQHPSK\ QUNRWQSYTT_WU`ZVbaWddXfgYhjZjm_lvQHsWYnfvp`mqWerRY\ sMQtHImRHf`G_jFUsFVpIVnLVlNVjQVhSWfVWdXWb_W`aWZdMe\ NWXfOHBXL`iNzdOz_OyWOyRPxNPwIPwEQv9Qu5QuFRnPSgYTag\ UVcBgogHp`LpUPqOTqHXrA`r4ds6as7_s9YsAWtCTtDRtEPtGN\ tHLuJIuKGuMEuNC8zihVckTbmSaoR`rP_tOZvNYzN_xMYuLXrL\ VoKUlKSiJRfJPcIO`INDSkLWeT_``cWhgQpkLxoGzrBboUAmkE\ gWIbGKcHMcIOcJPcJRcKTcLUcLWcMYcN_cO`cObcPdcQecQWRQ\ MEQC2QD3PE4OF5OG6NH7NI8MJ8MK9LLALMBKNCKOEJOGJQIISK\ IUMHVOHXQHZSG`UGcWGcXFcXF } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint