; Date: Wed, 31 Mar 2010 10:35:43 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 31-03-10 (Epsilon For Ever [6]) ; Id: <1.5.4.16.20100331093725.2a3f4104@pop.mindspring.com> ; --------- ; ; FOTD -- March 31, 2010 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's image lies in the Zexpe fractal, which is the fractal ; created by iterating the expression Z^(e)+C. There is nothing ; special about the number 'epsilon' when it is applied to ; fractals. Any other number in the same range would have created ; the same kind of parent fractal. The same is true of other ; significant but irrational numbers such as 3.1416... 1.618... ; and 1.414... These numbers may be of utmost importance in ; certain other applications, but in the world of fractals they ; and their kin are just so many more irrational numbers. ; ; I named the image "Epsilon For Ever". I was trying to think of ; a simple way of explaining to FL the significance of the number ; 'e' when I thought of the name. (The definition of other irra- ; tional numbers such as PI, the 'golden ratio' and the square ; root of two is easy to explain, but saying that Epsilon is the ; base of the natural logarithm begs the question of why this ; particular irrational number was chosen or even needed when the ; whole number 10 is far more intuitive and works just as well as ; a logarithmic base. (Or does it?) ; ; 'Epsilon' will remain forever mysterious, but today's image is ; no mystery. It is located in the chaos on the western side of ; the main bay of the parent Zexpe fractal. The image actually ; inherits a bit too much of this chaos. In fact, it inherits so ; much that it lacks a coherent theme, which is why I could give ; it a rating no higher than a 6. ; ; The calculation time of 5-1/2 minutes is near what the image is ; worth. The trip to the FOTD web site at: ; ; ; ; where the finished image may be viewed, is a true bargain. ; ; Tuesday turned most unpleasant here at Fractal Central as morn- ; ing clouds gave way to steady afternoon rain. The temperature ; of 41F +5C was made even more unpleasant by a biting northeast ; wind. The fractal cats didn't even think of the sun. They ; satisfied themselves by asking for an extra treat. ; ; My day was average, enough said. Unless Armageddon arrives, the ; next FOTD will be posted in 24 hours. Until then, take care, ; and do soles have souls? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Epsilon_For_Ever { ; time=0:05:29.03-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 float=y inside=0 center-mag=-0.7150857488907461/+0.119951277709464/\ 8.4e+007/1/-115/0 params=0/0/0/0/0/0/0/0/2.7182818\ 2845905/0 maxiter=5000 logmap=500 periodicity=10 colors=000ixOiyNhyLgzKfzIezGhz9ezFczL`zRYzXWzbUzaT\ z`Sz`Rz_QzZPzZRzYTzXUzWWzVXzUYzTZzSYzUXzVXzWVzVSzU\ QzTNzSLzRJzQGzPEzOCzN9zM7zLoz7mzAkzDizFgzIJzOJzPKz\ QKzQKzRKzSLzTLzTLzUPzWSzXWSZYU_`X`d_bgbcjedmhfpkgv\ mksmhpnfmncjn`gnYdnVbnTamT_lTZjTXiTWhTVgTTfTSdTQcT\ PbTNaTM`TL_TJZTIXTGWTFUTDTTCRTCQTBOUBNUBLUBLUBJVBI\ VBGVBFVBFWBEWBDWBEWBDWBDXBCXBBXBAXB9XB8XB8YB7YB6Y5\ 2YB6YG9UMDPRGL`KGkNCuR7zT1zW3wY4r_6l`7eb9dcBceCafE\ `gFZhGYiIWjJVmLRoMUqOcsPmvRwxSzzUyzVxzWxxTwwQwuNws\ LwpIvnFVZfVZiWYlWYpWXsWXvXYtXYrXYpYYoYYmYZkZZjZZhZ\ Zf_Ze__c__a`_``_Z`_X`_WcbYed_gf`ihbkjdmlepqpzzztrw\ vtlzyqzxovvlrtjoshkqfgoddnb`l`XjYUiWQgUMeSJdQFbOBz\ M8_K7ZJ7YJ6XI6WI6VI5UH5TH4SG4RG4QG3PF3OF3OF8QJDRNH\ SRMTVQUYVVaZWecXigYlXUbMQTBNJFKKILKLLKOKKRPKUUKYZL\ `cLehLimLrrLzvLzzLzzOzzRzzUzzXzz_zzbzzezzhzzkzznzz\ jzzfzzczz_zzXzzTzzQzzSzzQ } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;