; Date: Sun, 28 Jul 2002 10:58:09 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 28-07-02 (The Helm [7]) ; Id: <1.5.4.16.20020728105846.29e77262@pop.mindspring.com> ; --------- ; FOTD -- July 28, 2002 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; I named today's 7-rated image "The Helm" because of the ; resemblance it bears to a ship's wheel. ; ; Almost all my FOTD fractals are named after a resemblance they ; bear to a real-world object. This tendency to find the familiar ; in the unfamiliar is a universal human trait, perhaps best ; illustrated by the "faces in the clouds" illusion. ; ; No ship's wheel exists in today's image, which is merely a ; mapping to the screen of the number of iterations required ; before the iterated points of the image pass beyond the bailout ; radius. The coloring does not exist in the formula, but was ; consciously added by myself to enhance the resemblance to a ; wheel. ; ; Today's image is in fact nothing but one of the many ways in ; which the basic underlying mathematical abstraction could have ; been made manifest. The same formula could just as easily have ; created a piece of fractal 'music'. (Though I have yet to hear ; a piece of fractal 'music' that was worth being listened to more ; than once. [Or even once, for that matter.]) ; ; Today's generating formula -- 1.5(Z^1.1)+1.5(Z^11)+(1/C) -- is ; unusually simple. This is not surprising. When working with ; fractals, long convoluted formulae are unnecessary, and in fact ; often not worth the effort of writing them. Complex formulae ; are not needed, because the iterations work the magic. Great ; images come from skillful searching, not necessarily from 200- ; line-long formulae. ; ; The above statements are my personal opinion of course, ; especially the statement about fractal 'music' being worthless. ; Since beauty exists in the mind of the beholder, it may be that ; my mind is not tuned to the mental frequency of the appreciation ; of fractal 'music' and all the beauty in the music passes right ; through me like light through the invisible man. ; ; Forgetting the worth or non-worth of fractal music, the render ; time of today's image is a fast 3 minutes on my brave little ; P200 fractal machine. Approximately the same time will be ; required to download the completed GIF image from Paul's FOTD ; web site at: ; ; ; ; or from Scott's FOTD site at: ; ; ; ; The route to enjoyment of the image is left to the viewer. ; ; The weather Saturday here at Fractal Central was not perfect, ; but it could have been a lot worse. The temperature was held to ; a muggy 83F 28C by heavy clouds, which threatened all day but ; produced only a few drops of rain. The cats, who dislike high ; humidity, briefly checked the outdoor conditions, then decided ; to spend the day indoors. ; ; And I'm about ready to spend today relaxing. Until next time, ; take care, and where is that "Theory of Everything for Dummies" ; book? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ The_Helm { ; time=0:03:11.41--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-6.14601973153377700/-1.981123197536113\ 00/1.483931e+010/1/-28.746056810576011/-0.02765394\ 21627924401 params=1.5/1.1/1.5/11/0/0 float=y maxiter=900 inside=0 logmap=63 periodicity=10 colors=0006AI7AJ8AK9APAJUBMXCNcvl4kc8UNCzu8faBTODm\ A3`B7KBBk_ocTbWNVOHNb`dVSWNJNzfvbR`labcVXWOROHLu9x\ gAhUBUOZ9KNCDwBEcDFPErCkeB`TBQg_t`TiUN_NHP80PB4LE8\ I2Y_z8cj9X`ARQBLfl1FwzGfjGRVvrt1GQ6EMBCI6Y8AQBDIDq\ 1lnkYbZRRNLkwd`fWQRNLThIM6HI9GECHtkGYVY1dP6S9iPDSK\ RPJNKHJFG9W6CP9EIC1_p5Tf9NYDHOA3HD7G4q0jFk_D`QCQWr\ 8SgAOXCKMEFYGGMFKWYILOE6zF9bGDMmYVXMNv9H6HSBELsoZi\ dU_VPQLK9YikQ3WI9T1YjhRVSL24e77XC9O0eV8QNR_rOThLNZ\ IHPKZeIRXHJOrUOkpT`bOQPJYv_TjUPZPKNK__JTRHMJG5wdBZ\ SCQJDMIEIHFEG4pd7eYAWSDLLJOCfEM69P9AMBAKEBHTaSOTNK\ KJavGUfFNRFNboA5NC7KE9HdwuYjjSZ_MNP6JxBFa9nFDVFONZ\ Vy4Uba_h4TX8MMCP4MM6KK8IIAG5wK8jIBZHENGjwlvfomiddl\ UWoJNq8OuRPxhMflJdpGesHfjIgaIhUUiWejXqkYXl`CmbroaZ\ qQ4szAub1wKzyjnzbbzVRzNqz5gz8ZzAPzDzzPbzKQz83zK7zI\ AzHDzGYzBSzDMzEDzNszH_zG2zm7zaCzQxzflz_azTRzMOzELz\ FIzFQz2Nz6Lz9IzC6ztBz_OzW } 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================================== ; ;