But Jim, there *is* such a point circled by the planets. It is called Sun. Relativistically speaking, we can assume that the Sun circles the Earth every 24 hours... or not? ;) ----- Original Message ----- From: Jim M. <jamth@mindspring.com> To: <fractint@mailman.xmission.com> Cc: <philofractal@lists.fractalus.com> Sent: Thursday, May 01, 2003 10:14 AM Subject: [Fractint] FOTD 01-05-03 (Fractal Epicycles [8])
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:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Scott's site is found at:
<http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================
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