[Fractint] FOTD 21-09-07 (Squarely Rooted [5])

20 Sep 2007

      FOTD -- September 21, 2007 (Rating 5)

Fractal visionaries and enthusiasts:

Today's image takes us back to the MandelbrotBC2 formula and the 
complex logarithmic hyperspiralling ladder.  Today however we do 
not need the ladder, since we explore the Z^(sqrt(2))+C fractal 
at its ground level.

The parent fractal is a most curious Mandeloid, with a triangu-
lar period-2 bud as large as the main bay and an unusually long 
zig-zagging main spike extending far into positive-imaginary 
territory.

Today's scene is located deep in a valley separating the large 
triangular bud from a large sub-bud on its northern edge.  The 
depth of the scene in the valley makes today's image much slower 
than the FOTD images of recent days.

I named the image "Squarely Rooted" because its exponent is the 
square root of 2.  I rated it at a hum-drum 5 because it is 
plagued by the excessive chaos that is so typical of fractals 
with exponents of Z in the range between 1 and 2.

The calculation time of 12 minutes on the P4-2000mhz computer 
would be near one hour on the old P200mhz unit.  So why not 
visit the FOTD web site at:

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

and view the image effortlessly there.

Another typical end-of-summer day prevailed here at Fractal 
Central on Thursday.  The morning fog lifted by 10am, leading to 
a sunny afternoon with a temperature of 82F 28C.  The fractal 
cats made the most of it by lounging in the sun streaming in the 
southwest window for most of the afternoon.  My day was neutral.

The next FOTD will be posted for all it is worth right here in 
24 hours.  Until then, take care, and remember Fractint in your 
will.

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

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

Squarely_Rooted    { ; time=0:12:11.04-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 center-mag=-0.1234698959\
  7/+1.53149499923/3184551/1/90/3.88578058618805e-016
  params=1.4142/0/0/-97.25 float=y maxiter=7200
  inside=0 logmap=1174 periodicity=10
  colors=00060K60K60K70K70J70I80H80I80J80K90L90M90NA\
  0OA0PA0Q90RA0SA0TA0UB1TB2SB3RB4QC5PC6OC7ND8ND9NDAN\
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  sUitVlwVquWnsWlqXjoXhmXfkYdiYbhY`fZZdZXbZV`_TZ_RX_\
  PV`NU`LS`JQaHOaFMaDKbBIb9Hb7F_6EY6DW5CU5AS49Q48N37\
  L35J24H23F12D14E35E47E58E6AF7BF8DF9EFAGGCHGDJGEKGF\
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  qSjp_bngVmoNcxChwFmwIrwLvwOzwRzwUzwXzvWzvWzuVzuVzt\
  UztUzsUzsTzrTzrSzqSzqRzQH }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100, p=real(p2)+PI
  q=2*PI*floor(p/(2*PI)), r=real(p2)-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=========================================