FOTD -- March 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: Something is wrong with the following scenario, which I read many years ago, but I have never found the apparent flaw in the reasoning. In a certain town lying on the border between Mexico and the United States, a peculiar currency situation exists. In Mexico, ten U.S. dollars are worth only nine Mexican dollars, while in the U.S., the value of ten Mexican dollars is only nine U.S. dollars. One day a cowhand strolls into a Mexican cantina and orders a one-dollar beer. He pays for it with a Mexican ten- dollar bill and receives in change a ten-dollar U.S. bill, which is worth only nine dollars in Mexico. After drinking his beer he strolls across the border to an American saloon and orders another beer. This he pays for with the American ten-dollar bill, receiving a Mexican ten-dollar bill for change. He takes this back to the Mexican cantina and repeats the process, drink- ing beer merrily all day and ending up as rich as he started, with a ten-dollar bill. The question: Who paid for the beer. The moral: Forget about working and visit sunny Mexico. The conclusion: You can't get something for nothing . . . maybe. The solution: (IMO) Such an exchange rate is irrational. (But what if it actually existed?) And speaking of something for nothing, the same is true of fractals. The cost of today's image is 10 minutes calculation on a fast machine. The result is an image that must be seen rather than described. The holes in the diagonal blue background 'object' remind me of flatworms, which is why I named the image "Time for Flatworms". The rating of a 7 is close to correct. And don't be deceived by the apparent X-axis symmetry of the parent fractal. It breaks down on closer examination. Finally, if fractal calculation is not your cup of tea, visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image posted there. Sunday dawned clear but unusually cold here at Fractal Central, with a temperature of 23F -5C. But by afternoon the strong sun warmed it to 50F 10C, making things quite pleasant. The fractal cats spent most of the time by the heat. My day was slow and lazy, which leads to weird thinking, but things are due to perk up tomorrow. The next FOTD will be posted in 24 hours. Until then, take care, and where are those multiple universes when you need one? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Time_for_Flatworms { ; time=0:09:59.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.01019/0.00203573/18.69511/1/35/0 params=-0.5/-1.1/-0.5/-1.9/0/0/0/0 float=y maxiter=25000 inside=0 logmap=8 periodicity=10 colors=000wkYwjYviYvhYugYufYteYteYsdYscYsbYraYr`Yq\ _YqZYpZYpYYoXYoWYnVYnUYnTYmSYmSYlRYlQYkPYkOYjNYjMY\ jMYgOZdPZbQZ_SZYTZVUZTVZQXZOYZLZZG`XJ_ZMZ`OYaRXcTW\ eWWfYVh`UjbTkeSmhQpgRogSngSmfTmfTlfUkeUkeVjeVidWid\ WhdXgcXgcYfcZebZeb_db_ca`ba`baaa`a``b``b__cZ_cZ_dY\ ZeXZeXZfWYfVYgVYgUXhTXhTXiSWiRWjQWjQVkPVlOVlOUmNUm\ MUnMTnLToKToKSpJSpISqIRqHRrGSsERrFRrGRrHQqIQqJQqKP\ pLPpMPpMPoNOoOOoPOnQNnRNnSNmTMmTMmUMlVMlWLlXLkYLkZ\ Kk_Kk_Kj`JjaJjbJicJidIieIhfIhgHhgHghHgiGgjGfkGflGf\ mFenFenFeoEdpEdqEdrDcsDctDcuDcuDbvDavD`vD_vDZvDYwD\ XwDWwDVw8YyBWxDVwFUvHSuJRuMQtOOsQNrSMqVKqULqULqUMq\ UMqUNqUNqUOqTOqTOqTPqTPqTQqTQqTRqSRqSRqSSqSSqSTqST\ qSUqSUqRUqRVqRVqRWqRWqRXqRXqQXqQYqQYqQZqQZqQ_qQ_qQ\ _qR_rR_sS_tSauTcvUewUgxViyVkzWmzWmzXmzYmzYmzZmzZmz\ _mz_mz`mzamzamzbmzbmzcmzdmzdmzemzemzfmzfmzgmzhmzhm\ zimzimzjmzjmzkmzlmzlmzmmz } frm:MandAutoCritInZ {; 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)+(p4)), 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=========================================