FOTD -- May 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is titled "Minibrot for the Ages". This is admit- tedly an exaggeration, but the minibrot actually is the most impressive I have yet found in a Mandeloid with an exponent of Z less than sqrt(2). In today's image the exponent is a lowly 1.08. The parent fractal was calculated 16 levels up the complex- logarithmic hyperladder with the 'recip' function applied. Using this function probably defeats the original purpose of the formula, which was to create an animation of the different fractals that can be created from the different values of the multi-valued complex logarithm. This parent is shaped much like the minibrot in the image, though it lacks the prominent hook, and has a 'nose' on what would be the upper right side of its main bay. Today's minibrot is very large. In fact it is actually visible on the northeast shore line of its parent with only the slight- est magnification. The rating of an 8 might have been higher if I had devoted more effort to the coloring, which I admit is a bit haphazard. The image calculates is an unremarkable 3 minutes. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> Periods of sun interspersed with occasional thunder-showers made Friday an interesting day here at Fractal Central. The tempera- ture of 70F 14C was mild enough by winter standards, but rather chilly for late May in central Pennsylvania. The fractal cats had a typical day, though I think a bit of bad feelings arose between them in the afternoon. FL and I sometimes think of screening the back porch, adding shelves for the duo to leap onto, and making the entire porch into a catarium, where they can climb around and watch the world from their high, safe perches. The fractal cats appear to be ready for it. The humans had a frustrating day. We got word that one of our biggest customers will no longer be using our design services. This will leave more time for work on fractals, but less money for other things. Luckily, fractals are free and the supply of them is infinite. The next fractal will be posted in 24 hours. Until then, take care, and don't waste your energy worrying about things that have no chance of happening. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= MinibrotForTheAges { ; time=0:03:00.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=+0.106891367/+1.163747143/147.5/1/\ -178.25/0 params=1.08/0/16/525 float=y maxiter=12000 inside=0 logmap=158 periodicity=6 colors=000cKQaLPZMPWOOUPORRNOSNMTMJVMGWL6ZD9YGCYIE\ YLHZNK`PMaSPcUSdXUfZXh`_jcakedmhgojipljoijofjodkna\ kn_knXlmVlmSmlSmlRmlRlkQkjQiiQhhPfgPefXdeUcdSbcPbb\ N_YKYTIVOFSJDQEAG98A46mKzkFyj3ui5rh7ogDlWScLZUNdKP\ c4Rb9TaDVZIYWM_TRaQVcQXdPYePZfP`hQbkRdmSfoSgqRgsRg\ oTgkUegWccXb_Z`W_ZSaXObWKdUGeSAeS6eTDfRJgQPgPVhOai\ NgiMmjLskKykJubErV9nM4kE0gD5dDA`DFYDKUDPRCUNCZKCcG\ ChDCm93vACqALmAThAadAj_FyUDvVCtVArW9pW8nX6lX5jY2kX\ 3jY3iY4hY4gY5fZ5eZ5dZ6cZ6b_7a_7`_3Ep5MjATdK__UfUcm\ OmzEctJUpOQkSMgXQbaUZeYUjTPlaQniQopFqqLpqQprWor`os\ enskntpmyzzvwztuzqszoqzlovjmpgkceiVbgR`eOYcLWaIY_6\ U_FR_ON_WK_dH_lJZiLYgNYeOXcQXaSW_UWYVVWXVUZUSXQP_U\ QaXRc_SebTgfTiiUklVmoWorWkoXhmYzkzbhz_fzzezThzQkzz\ nzKqzHtzzwz4zz7zzzzzBzzCzzzzzDzzDzzEzzEzz0zzEzzRzz\ czzqzzpzzszzrzzqzzpzzozznzzmzzlzzkzzjzzizzhzzgzzfz\ zezzezzgzzizzkzzlzzizzfzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================