FOTD -- February 12, 2005 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image was named "Most Unusual Midget", but it was not really all that unusual, and rated only a 5. Today's image, which is named "The Right Path", would have been better named if it had been given the name of yesterday's image. It is the more unusual of the two. Today's image is located far to the northeast of the main part of its parent fractal, which is the same fractal that has given us the most recent images. The scene is located in a cut-off bit of circular debris inside a large closed ring that terminates the most prominent filament leading from the main part of the fractal. The image got its name from the narrow, winding path that encircles the central midget like a beltway encircles a city. It is truly a path to nowhere. One could travel it forever and never arrive at an end, for, like infinity, it has no limits. The concept of infinity is a strange thing. It is so easy to see that if one were to start traveling along the path in today's image, they would never come to the end because no end exists. Yet if one tries to imagine a straight line with the same endlessness, they find that their mind cannot grasp the entirety of the thing. Even harder to imagine is a half-line, a straight line with only one end. Is it infinite or not? We can see that a straight line with no ends would be longer, for it would extend into regions where the half-line did not. The answer depends on the direction in which we view the line. In one direction it is infinite; in the other direction it has a certain, though unimaginably great length. This half line situation reminds me of a day in seventh grade religion class in a Catholic school, when the nun was re-re-re- telling of how our souls will be perfectly happy in heaven forever if we obey God's commandments in this life. I asked the good sister how heaven could be fair, since those good people who died long ago have already had more happy time than those now living, and no matter how long we are all in heaven the ones who went there first will always have had more happiness than the late-comers. The sister replied that we will be looking forward to our future happiness when we get to heaven and not back to the hardships of earth life. She explained that everyone will be in heaven forever and will therefore have the same infinite amount of perfect happiness. I started to say, "but . . .", and the sister told me to sit down and shut up. Infinity is strange indeed. Any quantity can be added or subtracted from it and it remains unchanged. It can be multiplied or divided by any quantity, even infinity, and it remains unchanged. It can be raised to any finite power and it remains unchanged. (If it is raised to the power of infinity it might become a higher order of infinity -- I am not sure.) Well, I see myself again wandering from the topic, so it's time to note that today's image rates a pretty good 7 and renders in 2-1/2 minutes. It is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Weak sun and chilling winds here at Fractal Central on Friday kept the fractal cats indoors most all day. They did manage a brief 20-minute sojourn to the holly thicket to check for intruders. When they found none, they hurried back inside to watch the world from their shelf by the window. An extra large treat of tuna in the evening eased their disappointment. Today is looking like it will be another blustery one. The duo is braced for more disappointment. For me it looks like an average day coming up. But sometimes average days can be quite interesting. Check back in 24 hours to see if anything of interest appears in before then. Until next FOTD, take care, and if only we knew which path is the right one. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= The_Right_Path { ; time=0:02:25.11--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+5.20383959978280900/+2.454715711010205\ 00/286974.9/1/55/5.08479132410588619e-009 params=5/-1.26/0.5/-12.6/0/0 float=y maxiter=900 inside=0 periodicity=10 colors=000KgOGhPCiQ8jR4kS7lT9lUBmUDmVFmVHnWJnWLoXN\ oXPoYRpYTpZVqZXq_Zq_XhZV`ZUSZSKZRCZkBtiCqgCnfCldCi\ bDgaDd_DbYD_WEYUEUSEPQEMOEKMDIKDGLCECCCDBAEBAGAAHA\ AJ9AK9AM8BN8CP7DQ7ES9FTAGVCHWDIYFJZGKaILcJMfLNhMOk\ OPmPPoRQqSRsTRuXPs`NqdLnhJjkImoGrsEvwDzzBzzzzzzzzz\ wzRrwWmr`omeqhjrcolZjgUfbPbYKZTIUOHQJGMEFI9EECFDEF\ CHGCJGBMGAOHARH9TH8WI8YI7`I6bJ6eJ5gJ5cN9_QDWTGSXKO\ _NKbRGfVCiY8la4od3oc3ob3oa3oa3o`3o_3o_2oZ2oY2oX2oX\ 2oW2oV2oV1oU1oT1oS1oS1oR1oQ1oQ5mT9lWDkZHi`LhcPgfTe\ hXdk`cndaph`sl_voZxm_yk`yjayhayfbyecyccybdy`eyZeyY\ fyWgzVhzThzRizQjzOjzNkzLlzJlzImzGnzFnzIlxKkwMivOhu\ QgtSesUdrWcpYao_`na_mdYlfXkhYjjZhl_gnafpceredtgcvi\ bxkavmbtobrqbpsbnuclwckyciycgzdezdczdazd_zeZzeXzeV\ zeTzfRzfPzfNzfMzfMzdMzcMzaaz5`z4_z6Zz7Yz8Xz9WzAVzC\ UzDTzESzFRzGQzHPzJOzKNzLMzMLzNKzPJzQIzRHzSGzTGzUJz\ RMzOPzMSzJVzHUzGTzFTzESzD } 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=========================================