;     Date: Tue, 03 Jun 2003 08:56:23 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 03-06-03 (Unity and a Half [6])
;       Id: <1.5.4.16.20030603085556.2b6fa83c@pop.mindspring.com>
; ---------
; 
; FOTD -- June 03, 2003 (Rating 6)
; 
; Fractal visionaries and enthusiasts:
; 
; We seem to be developing a theme for the month of June.  I had 
; no intention of having two 'theme' months in a row, but 
; sometimes fractals have a will of their own, and a theme of 
; midgets in the many Z^(1.5)+C fractals seems to be developing.
; 
; Today's image is the third consecutive scene in the set of 
; fractals created by the formula Z^(1.5)+C.  As the lengthy 
; real(p2) parameter shows, the parent fractal was found by the 
; evolver feature.  I could have rounded off this parameter to 
; -46.7 with little change in the resulting image.
; 
; Fractals with exponents in the X.5 range are the most prone to 
; the type of discontinuities that fill today's image.  Fractal 
; discontinuities decrease in significance as the exponent nears 
; integer values, and vanish entirely when the exponent is an 
; integer.  I normally use the <floor> function with the 
; MandelbrotBC1 formula, but for a change, I used the <recip> 
; function in today's image.
; 
; In today's image, which lies in the most-discontinuous range of 
; exponents, the attractive symmetrical patterns that surround 
; midgets in the classic Mandelbrot set are totally absent.  
; Today's half-midget is surrounded by a kind of star-burst with 
; an obvious break in the upper part.  This break totally destroys 
; any pretense of symmetry, though it does make an interesting 
; feature.
; 
; To add more interest, I rendered the image with the outside set 
; to < fmod > and the proximity set to 0.5.  The other outside 
; options also make interesting variations of the basic scene, and 
; are worth checking.
; 
; I named the image "Unity and a Half" as a description of the 
; exponent.  I could rate the final result at only a 6.  The 
; rating is held down by the coloring, which could have used a bit 
; more work.
; 
; At least, the render time of 6 minutes is reasonable.  The 
; download of the finished image file is even more reasonable.  
; That download can be found at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; Another perfect day here at Fractal Central on Monday produced 
; perfect cats.  The not-quite-dynamic duo spent the better part 
; of the day in their porch chairs, watching the world, enjoying 
; the temperature of 73F 23C, and remembering the days when they 
; were actually dynamic.
; 
; Today, unfortunately, is starting cloudy, with rain promised by 
; afternoon.  For me, it will be just another workday.  Until next 
; time and next fractal, take care, and sometimes fractals are not 
; all they're cracked out to be.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Unity_and_a_Half { ; time=0:06:08.50--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=recip passes=1
  center-mag=-0.73254313764763500/+0.180334958341697\
  00/4.605696e+007 params=1.5/0/-46.74114200262459/0
  float=y maxiter=4200 inside=0 proximity=0.5
  outside=fmod symmetry=none periodicity=10
  colors=000CvNBnPBfRBZTASVAKXACZA5`WSZpnYokZnhZmeZl\
  bZk_ZjX_iU_hR_gO_fL_eI_TFYHCXMIYQNYVSYZXYbaYgfYkkY\
  opYkk`gfccae_XhXSjTNmPIpLDrH8uE4wF6rF7mG9hGAcO8TV6\
  Ia47WGFQSMKcUEo`9zgBxcCv`DtYErVGpSHnPIlMJjJKiGPlJU\
  nMZpPcrShtVmvYks_ipagmcfjedggbdi`ak_ZmYWoWTqUQsTNu\
  RPrPQoOSmMTjLUhJWeIXcGY`E_YD`WBaTAcR8dO7eMBcOEaPI`\
  RLZSOYTNTRMPPWnaSoYOpVJqRFrNBsK7tG3tD5qE6nF8lG9iHB\
  gICdJEaKF_KHXLIVMKSNLPONNPOKQPIQY9Kf1Fg7DgCCgIBhNA\
  hT9hY8ic7ih6im5ciAYfFScJN`OHYTBVX5Sa0Pe3Of6Og9OhBO\
  iEOjHOkJOkMOlPOmROnUOoXOpZOp_Kl_Hh_Dd`A``6X`3T`0Qb\
  2Td3Ve4Xg6_h7aj8ckAfmBhoCjpEmrFosGquItvJvxKxyLzwOy\
  vQxuSwtVvsXurZtqaspcroeqnhpmjollnkomjqlislngkrWkUg\
  W6sGBcSGOcL8nODmQHlTMkVRjYWi__iadhdhgfmfiqekudiwib\
  vkbti_odWj_TfVQaQMXLJTGFOBCJ69F1BE2CE3ED3FD4HC4IC5\
  JB5LB6MA7OA7P98R98S89T89SBBSDCSGESIFSKHRNIRPKRRLRU\
  MRWOQZPQ`RQbSQeUQgVQiWJpR }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(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==================================
;