; Date: Thu, 01 May 2003 09:14:17 -0400 ; From: "Jim M." ; Subject: [Fractint] FOTD 01-05-03 (Fractal Epicycles [8]) ; Id: <1.5.4.16.20030501091325.29e7a8b6@pop.mindspring.com> ; --------- ; ; FOTD -- May 01, 2003 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; This is the day, the day fractal fans have been waiting for with ; bated, but not abated, breath -- the day the FOTD resumes its ; one-a-day schedule. And we start with a fractal that earns a ; lofty rating of 8. I named the image "Fractal Epicycles" for no ; good reason. I simply liked the sound of the title. ; ; An epicycle is not an epihertz. It is not an electronic wave at ; all. It is a revolution around a moving point. Before men under- ; stood the true nature of the solar system, the retrograde loops ; the planets trace in the sky when they are near opposition were ; assumed to be a result of the planets circling a point that in ; turn circled the earth. As we discovered later, this is not so, ; and epicycles fell from favor, eventually going the way of the ; luminiferous aether. ; ; Today's image is a zoom into the curiously symmetrical image ; posted by Lee Skinner about 5 days ago. I lowered the bailout ; radius to 30, but left the other parameters unchanged. ; ; In fractals generated from formulae that contain negative powers ; of Z, the value given the bailout makes a huge difference in the ; final appearance of the image. Increasing the bailout causes ; the elements to shrivel and break into separate pieces which ; eventually shrink to nothing, leaving an image that consists ; entirely of 'inside stuff'. But even when the elements have ; 'evaporated' the ghost of the original image can still be raised ; by setting the inside fill to something like bof61. This ghost ; is sometimes the best version of the scene, though in today's ; image it is too chaotic and far too slow. ; ; Decreasing the bailout has the opposite effect. The elements ; increase in size until one expands to fill the entire screen, ; resulting in an image of a single featureless color. Using an ; outside coloring method other than the standard equal-iteration- ; bands occasionally results in an interesting variation, though ; this is the exception rather than the rule. ; ; Today's image renders in a relatively modest 7-1/2 minutes on my ; aging and overworked P200 machine, the one with the noisy ; exhaust fan that needs a pep talk to make it start turning. The ; finished GIF image is available on the two FOTD web sites, which ; have been slow lately, but will become more active now that the ; daily FOTD is back. ; ; The URL of Paul's site is: ; ; ; ; Scott's site is found at: ; ; ; ; The weather here at Fractal Central on Wednesday was fractal in ; nature, as it always is. The warm sun and temperature of 75F ; 24C brought out the best in the fractal duo, who passed most of ; the afternoon in the yard and on the porch, watching for ; intruding cats. At one time, the cat that lives three doors ; down the hill thought of walking through the duo's yard. His ; thoughts were quickly laid to rest when Tippy leaped to the ; attack position. Thomas observed the goings on with interest, ; presumably ready to run to help, (or more likely, for help), if ; things got too far out of control. ; ; Today is starting far less pleasantly, with lots of clouds, and ; rain threatening. On such days, the duo usually stays indoors, ; while I try to finish the work that needs to be done. And right ; now, I have enough to be done to keep me busy most of the day, ; so until next time, which will arrive in 24 hours, take care, ; and if an infinity of other me's exist somewhere out there, what ; practical difference does it make? After all, I will never meet ; them (or me). ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Fractal_Epicycles { ; time=0:07:39.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.60678114611431010/+0.052890451621420\ 53/1894179/1/137.5/1.24117062995365846e-007 params=-3.7/-1/-1.6/-2/-0.4/-70 float=y maxiter=4500 inside=0 logmap=120 periodicity=10 colors=000PKsfRshTsKKrKKpIAoKKsFKnFGmDHkCIjAJi9Kh8\ Lg6Mf5Ne3Od2Pc1Pb7OaCN`IM_NLZTKYYJXcIWhHVnGUsFTxES\ yJPyOMyTKyYHzbEzgCKz9zzzzz4mpztUAqhDncGk_JhWMeSPbN\ S000000000000000000000000000000000000000000000000d\ A`zmUlC`lGZlKXzzVmTSmXQnaOneMniKkdMh`NeWObSQ_NRXJS\ YGbZEldPmjZnohnpijqjgqkdrk`slYsmVtnRunOuoLvpHwqEwq\ BrpDnoFjnHfmJamKYlMUkOQjQLjRHiTDhV9gX5gYCfbIfgOelU\ eqXfl_fhbgceg_hhWkhRniNqiItjEujAwiByhCzgDzfEzeFzdG\ wcHrcImbJhaKf`Le_McZNbYO`XP_XQ_VO_TN_RM_PK_NJ_LIXN\ HVOGSPFQRENSDLUDIZCGcBDhABm99m9CrBEcDGSFIPPKNUMLZO\ IcQGhSEmUBrW9wY7z_4za2zc0z`2ZY4XV5VS7TP9RMAPJCNGEL\ DFJAHH7IFBJGFKGJLGNMHRMHVNHZOHbPIfQIjSInUJrWJvYJz_\ JzaSzc_zegzgozimzkkzmizogzqfzsdzubzw`zx_zy`zzZzzXz\ zVzzTzzRzzPzzNzzLzzJzzHzzFzzDzzBzzGzzKzzPzzTzzYzza\ zzYzzVzzRzzOzzLzzTzzVzzXzz_zzazzczzfzzhzzjzzlzznzz\ ozzqzzrzzszzszzszzszzszzs } frm:MandelbrotMix4 {; 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, 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================================== ;