######################################################### Jim Muth often makes a comment about the appearance of the parent fractal that a FOTD image is calculated from. His description of today's FOTD encouraged me to create the parent fractal:

FOTD -- March 27, 2007 (Rating 6)

Today's parent fractal came about when I combined 0.1 part of Z^(10.5) with 1 part of Z^(1.05) and added straight C. It reminds me of a Mandelbrot set with a clumsily trimmed peacock's tail. ... Today's scene is located in the peacock tail.

The .PAR file below to create the parent image with the peacock's tail was easily created by: - calculating Jim's March 27th, 2007 FOTD, - repeatedly hitting <PgUp>, making the zoom box be as small as possible, - hitting the key combination <ctrl><enter> to calculate the new image formed when the original full screen-sized FOTD is shrunk to the size of the tiny zoom box -- ('zooming out' instead of 'zooming in'). - repeating the 2 previous steps until the original 'peacock's tail' image described by Jim appears. - hitting the <B> key to write the .PAR file. I have oriented the parent fractal differently than Jim did (I rotated and translated it) in the image created by the PAR file below -- to fit as much of it into a 3:4 aspect ratio image as possible. With this particular image if you create the parent fractal yourself, note that as you repeatedly zoom out you create a couple of completely dark blue screens. Have faith and zoom out 3 or 4 more times and you will see the 'clumsily trimmed peacock's tail" attached to the Mandelbrot set described by Jim. Feel free to rotate and translate the final image to better frame it as I did in the .PAR file below. To speed the process up, note that you do NOT need to wait for the current image to complete its calculation before you repeatedly hit <PgUp> to make the zoom box be the smallest it can be -- before hitting <ctrl><enter>. Here are two ways to get to Jim's 'clumsily trimmed peacock tail': 1) Give the PAR file for Jim's peacock tail below a try -- it only takes 30 seconds to calculate on a 400MHz Pentium II. 2) Also, please let me know of your success (or lack thereof) if you try the sequence of steps given above to get to the peacock tail. Be sure to use Jim's original FOTD PAR for March 27th, 2007 to create the first image and NOT the PAR below before you start zooming out. - Hal Lane ######################### # hallane@earthlink.net # ######################### START PARAMETER FILE======================================= FOTD27Mar07_parent { ; Hal Lane 07-03-27 0:31 P400 1024x768 ; Parent fractal of Jim Muth's Fractal ; of the day. Corresponds to the full ; Mandelbrot set image. MandelbrotMix4 ; "...a Mandelbrot set with a clumsily ; trimmed peacock's tail." - Jim Muth ; reset=2004 type=formula formulafile=_pastarc.frm formulaname=mandelbrotmix4 function=ident center-mag=0.0155095/0.0158911/4.411155/1/158.999999879\ 58455/1.08116875563446513e-007 params=0.1/10.5/1/1.05/0/0 float=y maxiter=300 inside=0 logmap=45 periodicity=10 sound=off colors=000AAUAAKAAUAAKAAUAAKAAUAAKAAUAAKAAUAAKm00h09c0B\ Z00U00zzmzmLzzmzm0zzmzm0_imHU02D0DJ0PP2aW6na9zeBaeJDzR0\ e_0ee0Yl0Rr4LyyzzR9zc4zn0zRBr8OR0a2zy00Y00H0040000000zl\ pyizyizWz0Ou2FiH8_Y0Pn0Fz08zwz0rz0pzFlwUiniggyzezzczzca\ wcFgc0Wc0JP08B0006<2>00Y00c2Di9PpHcwPpz0Up09e02c00a20_9\ 0_Pzp0Hn00n00n00n00n02n09n0Fn0On0Un0Wi0Wg0Yc0Ya0YY0_W2_\ R2_P4WU6UY8Ra9PcBOgDLlFJpHHrJWnLilOyiPzgRzeLzcHzaDzaBzc\ 9ze8ze6zg6zgFznPzu_zzizzuzzazuJze2zR<2>8zMAzKBzHDzFFzFO\ zJUzL_zOUzYPzeJznFzy9zz6zz0zz0zz0zz4zrLzcazPUzJLzDDz86z\ 20z00z9<2>0zr0zz0zzDzzRzweziuz_uzauzeuzguzluznuzpuzuuzw\ uzyizn_zcPzWFzL8zD0z40z0<4>0z0<4>0z0<3>Hz0Dz4Bz69z88zB4\ zD2zF0zJ<3>0zU0zW0zY0z_0za4zc6ze9zgDziHzlJznOzpRzrWzuYz\ wWzrUzpUzlRziRzePzcOz_OzYLzULzRYzJgzBrz4zz0yz0uz0pz0nz0\ jz0ez0az0_z0Wz0Rz0Oz0 } 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======================================= ######################################################### -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.413 / Virus Database: 268.18.18/734 - Release Date: 3/26/07