;     Date: Sun, 09 Feb 2003 09:22:38 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 09-02-03 (Irregular Minibrot [5])
;       Id: <1.5.4.16.20030209092548.29eff578@pop.mindspring.com>
; ---------
; FOTD -- February 09, 2003 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's fractal is named "Irregular Minibrot".  The reason for 
; the name is the shape of the midget and the irregularity of the 
; features around it.  The midget is irregular because instead of 
; iterating Z^2, I iterated Z^sqrt(2) and chose a spot 14.142 
; levels down the logarithmic spiral to do the rendering.
; 
; When this low a power of Z is iterated to make a fractal, the 
; results are totally unpredictable.  Mandeloids generally have a 
; number of lobes one less than the exponent of Z in the 
; generating expression.  Thus the formula Z^5+C draws a Mandeloid 
; with 4 lobes, and the Z^2+C Mandeloid, which is the classic 
; Mandelbrot set, has one lobe.  Following this progression, the 
; Z^1.4142 Mandeloid has only 0.4142 lobe, less than half a lobe, 
; but there is no easy rule determining which fraction of a single 
; lobe will appear either in the parent fractal or in the midgets 
; it contains.
; 
; Theoretically, today's midget is only less than half there.  Its 
; buds are smaller than those of the classic M-set and more widely 
; spaced.  In addition, the buds are in the wrong places and mis-
; shapen as well.  There are several smaller midgets in the image, 
; which are easily found by toggling into and out of color mode.  
; Some of these may also be interesting.  I have not checked to 
; see.
; 
; With all its imperfections, today's FOTD makes an interesting 
; image, though not interesting enough to rise above the rating of 
; an average 5 that I gave it.  The render time of 7 minutes is 
; fair enough for such a mediocre image, and most of that time can 
; be saved by downloading the fully-rendered GIF image from one of 
; the FOTD web sites at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; The weather remained sunny all day Saturday here at Fractal 
; Central, but the temperature of 25F -4C proved far too extreme 
; for the whiskers of the cats, who poked their noses out the door 
; only long enough to sample the chill and determine that they did 
; not want to be outside.  Today is starting warmer, but it is 
; cloudy, so the effect on the dynamic duo will likely be the same.
; 
; I have nothing much planned for the day, other than exploring 
; Fractal Land that is, so I'll take it an hour at a time.  Until 
; next FOTD, take care, and can the shape of fractals be 
; influenced by the power of thought?
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Irregular_Minibrot { ; time=0:07:26:88--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=+0.86416652796344500/+0.512463707154294\
  50/1904.762/1/67.5/-5.01217123360930827e-012
  params=1.4142/0/-14.142/0 float=y maxiter=6000
  inside=0 logmap=73 periodicity=10
  colors=000SZSQYROXQMWPKVOIUNFTMCSL9RK6QJ3PH4OI4NI4\
  MI5LI5KJ5JJ5IJ6HJ6GK6FK7FK7EK7DL7CL8BL8AL89M98M97M\
  96M72L84M96MA8NBANCCOCEODGPEIPFKQGMQHORHQRISSJUSKW\
  TMYTOYTQXVSXWUWXWWXYVY_VZaU_cU_eT_gT_iS_kR_mQ_oP_m\
  OYkNXiMWfLVdKUbJU`ITYHTWGSUFSSESPDRNCRLBQIAQG9PE8P\
  C8O97O77N57N37N49N5AN5CN6DN7EN7GN8HN9IN9KNALNBMNBO\
  NCPN5PQCQNIULPXJV`GacEggCmjAnhBngCofDoeEpdFpcGqbHq\
  aIr`JsYGrZIr_Jr`KraLqbMqcOqdPqeQpfRpgSphTpiVpjWokX\
  olYomZon`noanpbnqcnrdpxcnselnfkjhieig`jfXldSmbOscO\
  pcOndOldOidOgeOeeOceO`fOZfOXgOVgOSgOQhOOhOMhOJiOHi\
  OFoIAiODdTF_ZIVcKQiNLnPGsRKnQOjRSeSV_TZXUbWVfUWeWX\
  eYYd_Zda_cc`ceabhbbkcandaqe`tfdwgbzh`ziZzjXzkVzlTz\
  mRznPzoNzpLzqJzrHzsFztDzuBzv6zwAzxEzyIzzMzzQzzUzzX\
  zz`zzdzzhzzlzzpzztzzxzzwzzwzzwzzwzzwzzwzzyzzwzzuzz\
  szzqzzozzmzzkzzizzgzzezzczzazz_zzYzzWzzUzzSzzQzzOz\
  zMzzKzzIzzJzzHzzGzzFzzDzz }

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==================================
; 
;