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: <http://www.Nahee.com/FOTD/> 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=========================================