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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's FOTD site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================