[Fractint] FOTD 24-07-08 (Ratcheting Onward [6])

24 Jul 2008

      FOTD -- July 24, 2008 (Rating 6)

Fractal visionaries and enthusiasts:

I have made a decision to stay more on topic.  Starting today I 
will no longer post a copy of the FOTD to the philofractal list. 
Except for the FOTD, the philofractal list has been dead for 
years.

The topic of the Fractint list is fractals, not my ideas about 
God, science, or the paranormal.  There are quite a few forums 
where these things are eagerly and properly discussed.  And I'm 
not too sure of the importance of the daily weather report from 
central Pennsylvania, which can always be found on the internet.  
If the goofy fractal cats do anything exceptionally goofy, I'll 
tell about it however.  (Yes, FL did have something to do with 
my decision to stick more to the topic.)

Today's image shows some of the unexpected stuff that goes on in 
the fractals created by the formula Z^(1.075)+C.  The most 
surprising thing about these almost-linear fractals is that they 
actually contain fiercely detailed Minibrots, which can be 
easily found with my 'secret' method of finding minibrots.

One of these unlikely minibrots lies at the center of today's 
image, at the very limit of resolution.  I have not gone deep 
enough to make the minibrot visible in today's image because at 
that depth, the surrounding pattern breaks down into near total 
chaos.

At the modest magnitude of today's image, the pattern is far 
more interesting, rather resembling a ratchet wheel surrounded 
by a lacy network of lightning.  I named the image "Ratcheting 
Onward" because of the ratchet pattern.  This heavily fractured, 
circular effect is typical of the minibrots in fractals of such 
a low order.

The rating of a 6 is what I think the image deserves.  The 
calculation time of 1-2/3 minutes is a real bargain.  An equal 
bargain may be found at the FOTD web site at:

       <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

where the finished GIF image is posted.

Until next time, take care, and keep a stiff upper fractal.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

START PARAMETER FILE=======================================

Ratcheting_Onward  { ; time=0:01:41.60-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=-14.94607802098338/-2.324758141946301/\
  8252035/1/-162.5/0 params=1.075/0/18/1500 float=y
  maxiter=1800 inside=0 logmap=131 periodicity=10
  colors=0009G06H0AI6DJFHDKKKZOPdRVmUfuZitzksonrwnqz\
  uphVsZ9uX8pV7lU7hS6dR6`P5XU5Tc6Nm6Zr6Zz6Zz6ZIlq3Wp\
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  wc_xc_yc`zc`ycaycaycbycbyccxccxccxcdxcdxcewcewcfwc\
  fwcfwcgwcgvchvchvchvcivciucjucjuckuckuckucltIltImt\
  ImtIntInsInsIosIosIpsIptHqsIpsIpsIprIprIprIorIoqJo\
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  4bg6bg7bg8bgAbgBbgCbgEbgFbgHbgIbgJbhLbhMbhNbhPbhQb\
  hRbhTbhUbhWbhXbhYbh_bh`bi }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

END PARAMETER FILE=========================================