; Date: Wed, 18 Oct 2006 06:45:46 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 18-10-06 (Double Trouble [6]) ; Id: <1.5.4.16.20061018064712.0dcf4172@pop.mindspring.com> ; --------- ; ; FOTD -- October 18, 2006 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's fractal is kind of a mystery. I'm not sure if it is a ; real fractal or an artifact. The formula is simply a variation ; of the hypercomplex formula in fractint.frm, with a few more ; variable parameters added. The strangeness lies in the imag(p3) ; parameter, which is 10^(-012). It seems unlikely that such a ; small value could make such a big difference in the appearance ; of the parent fractal. I suspect that we may be dealing with ; some kind of mathematical imprecision here, but if so, I have no ; idea what it might be. ; ; Regardless, the fractals the formula creates appear as real as ; any other fractals. They may be zoomed into up to the limit of ; double-precision math, though the fact that the periodicity must ; be set to zero hints that the fractal-reality of this fractal ; might be questionable. ; ; It's a rather somber image, with a pronounced 3-D effect, which ; looks its best when the screen brightness is turned well down. ; ; I named the image "Double Trouble". It comes in two halves and ; there is always that troubling doubt about its validity. The ; rating of a 6 seems appropriate. ; ; The render time of just under one hour is necessary due to the ; large maxiter of 15000 and the necessity to turn off periodicity ; checking. But this time will be cut to 10 minutes or so on the ; fastest machines. If even this is too slow however, it would be ; best to wait until Paul posts the finished GIF image to the FOTD ; web site sometime later today. The web site may be accessed at: ; ; ; ; A steady chilly rain fell all day here at New Fractal Central on ; Tuesday. The fractal cats spent a good part of the day watching ; the cars splashing by. In my department, the big rush job that ; is supposed to be soon coming in has so far failed to appear. ; It is still promised this weekend however, so we'll have to see ; how it goes. The next fractal will go as scheduled in 24 hours, ; I presume. Until then, take care, and the crazy schedule will ; soon be over. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Double_Trouble { ; time=0:59:28.63--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=HyperSquare passes=1 center-mag=-0.17649147506615800/0/2086.338/1/90/\ -1.23373533611470521e-014 params=0/0.5/10/0/0/\ 1e-012 float=y maxiter=15000 inside=0 logmap=443 periodicity=0 colors=000UFKUDJUBIUBIUAHUAHU9HU9HU8GU8GU8GU7GU7GU\ 6FU6FU5FU5FU5FU4EU4EU3EU3EU1FU2EU3EU4EU5EV6EV7EV8D\ V9DVADWBDWCDWDDWEDWFCXGCXHCXICXJCXKCXKBYKBYKBYKBYK\ BYKBYKBYKAYKAYKAYKAYKAYKAYL9YM9YM9YN9YO9YP9YQ7YR8`\ R8`S9`R9`RA_QA_QB_PB_PC_PCZPDZPDZPDZPEZPEYPFYPFYPG\ YPGYPHXPHXPIXPIXPJXPJWPJWPKWPKWPLWPLVPMVPMVPNVPNVP\ OUPOUPOUPPUPPUPQTPQTPRTPRTPSTPSSPTSPTSPUSPUSPURPVR\ PVRPWRPWRPWQPVQPVQPVQPVQPVSQVRPVQPVPOVPOVOTUNSTNSS\ MRQLRPKRNKQMJQKIQJIPIHPGGOFFODFOCENADN9CO7DN8EN8FN\ 8FN9GN9HM9HMAIMAJMAJMBKLBLLBLLCMLCNLCOKCOKDPKDQKDQ\ KERJESJESJFTJFUJFUIGVIGWIGWIHXIHYHHZHHZHI_HI`HI`GJ\ aGJbGJbGKcGKdFKdFLeFLfFLfFMgEMhEMiEMiENjENkDNkDOlD\ OmDOmDPnCPoCPoCQpCQqCRqCSpDTpDUpEVpEWpEXpFYpFZpG_p\ G`pGapHbpHcpIdpIepIfpJgpJhpKipKjpKkpLlpLmpMnpMopMp\ oNqoNroNsoOtoOuoPvoPwoPxoQyoQzoRzoRzoRzoSzoSzoTzoT\ zoTzoUzoUzoVzoVzoVzoWzoWz } frm:HyperSquare {; Jim Muth a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel b=p2*a*b+p3 a=q, |a|+|b| <= 100 } ; END PARAMETER FILE========================================= ; ;