; Date: Fri, 28 Aug 2009 16:07:00 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 29-08-09 (Various Distortions [No Rating]) ; Id: <1.5.4.16.20090828160920.2bc7b316@pop.mindspring.com> ; --------- ; ; FOTD -- August 29, 2009 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; Check the philofractal list for a longer discussion. ; ; Today's image is more a fractal study than any kind of art work. ; But as a combination of Z^2 and Z^(-2) it is still worth a look. ; ; The image is named "Various Distortions". I gave it this name ; when I saw in it the three types of distortion that can afflict ; Mandeloids. These distortions surely have sound mathematical ; causes, but other than the non-critical type of distortion, I ; have no idea what these causes might be. ; ; The first type of distortion appears in the dark Mandeloid ; fragments vaguely showing in the background in the northeast and ; southeast parts of the fractal. This distortion appears when ; the starting point of Z is set to a non-critical value. This ; particular distortion can be readily seen by calculating the ; type=mandel Mandelbrot set and setting the parameters to ; something between zero and one. The distortion simply cuts off ; part of the set. ; ; The second type of distortion is clearly visible in the two ; prominent Mandeloids on the X-axis. In the Mandeloid on the ; left, the main period-2 bud is too large and the higher-order ; buds are bunched toward East Valley, while in the Mandeloid on ; the right, the main bud is too small and the higher-order buds ; are spread out toward the main bud. I have no idea of the ; mathematical cause. ; ; The last type of distortion is visible in the two smaller ; asymmetrical Mandeloids at the top and bottom of the image. ; In this case the entire system of buds is skewed to one side or ; the other. In the buds in the image, this skewing is not too ; severe, but it sometimes becomes so severe that the main ; period-2 bud is impossible to find without checking the actual ; orbits of the points. Once again I have no idea of the cause. ; ; Since the image is more a mathematical study than a work of art, ; I could give it no rating. But with a calculation time of under ; 15 seconds, at least on my recently rehabilitated middle-aged ; 2000mhz machine, there is no reason for anyone to miss seeing ; the distortion. ; ; Of course, the trip to the FOTD web site at: ; ; ; ; is still more fun than calculation. ; ; Heavy clouds and periods of rain spoiled Friday here at Fractal ; Central. The temperature of 70F 21C was irrelevant. The fractal ; cats checked the outside several times, but when they saw too ; much rain and no sign of the end of the world. they went back to ; sleep. ; ; My day was rather busy but not frantically so. The next FOTD is ; scheduled to be posted in 24 hours. If an unexpected antiquing ; expedition comes up, the FOTD might be delayed however. Until ; next time, take care, and prepare. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= VariousDistortions { ; time=0:00:14.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.861346/0/0.814578 params=0.1/-2/0.55\ /2/0/0/0/0 float=y maxiter=350 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000wkCri0mg3he6cc9ZbCU_BPXAKU9FR9ANH5JO1FV1\ Ba07h03z9DzINzQXzZfzfpzamzXjzSgzNdzIazDZz8Wz4UzCQz\ KNzSJz_GzgDz_AzS8zL6zD4z62zWSzMBzNAzNAzNAzNAzNAzNA\ zNAzNAzNAzNAzNAzNAzNAzXSzehncimajl_jkYkjWliUlhSmgR\ mfPneNodLocJpbHqaFq`Dr_CrZFs_Ht_Ju_Lu_Nv_Qw_Sw_Ux_\ Wy_Yy_iwOuvDtrFsoHrlJqiLpfNobPn_RnXSmUUlRWkNYjK_iH\ ahEchBdiEejGekIelLemNemPenSfoUfpWfqZfr`frbfodble_j\ fXghUeiRbjO`lLYmIWnFTpCRq9Or6Ms3Pp4Rn5Tk6Vi7Xf8_d9\ aaAc_BeXCgVDjSElQFnNGpLHrIItGJvPXxYjzexzguzhrziozj\ lzkjzlgzmdznazoZzpXzqUzrRzsOztLzuJzvLDwzFxzGyzIzzJ\ zzLzzMzzOzzPzzRzzSzzUzzVzzWzzTzzQzzOzzLzzJzzGzzDzz\ Bzz8zz6zz9zzBzzDzzFzzHzzJzzLzzNzzPzzRzzTzzVzzTzzRz\ zQzzOzzNzzLzzKzzIzzHzzFzzEzzCzzBzkEzeGz`IzWKzRMzMH\ zKCzI7zG2zE7zFBzGFzHJzIOzJSzKWzL_zMczIfzEizAlz6oz2\ gz3_z4Sz5Kz6Cz79z67z65z53z51z5vzNqzOlzPgzQbzRYzSTz\ TOzUJzVEzW9zX5zYCzZWzUSzP } 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint