Fractal visionaries and enthusiasts: 

Today's image shows a minibrot lying way out near the tip of the main spike of its parent fractal.  But this parent is not the Mandelbrot set.  It is a Z^(1.333)+C fractal with a spike that puts the spike of the M-set to shame.

To begin, the spike is far longer than the M-set's spike, and it also points northwest instead of straight west, with far more fractal detail along its path.  With all these superior features, I could consider the spike nothing less than super, which was reason enough to name the image for its location -- "On the Superspike".

The parent fractal came about when I calculated the expression Z^(1.333)+C at a height of only one level up the hyperladder (or hyperspiral) with the cosine function applied.  I think this is the first time I have applied the cosine function to the MandelbrotBC3 formula, and at today's hyperlevel it produces a rather scrambled parent with little but its one superspike.

The image came about as a result of an effort to duplicate the rating of yesterday's image, but the final result was less impressive, rating only a 7 for both art and math worth.

The image is a super fast one, finishing in 20 seconds or less on a SOTA (State Of The Art) machine.  Even on older units it will finish very fast.

Heavy clouds spoiled the first half of the day here at Fractal Central today, while rain spoiled the second half.  The temperature of 57F 14C was quite reasonable for the season however.

The next FOTD will soon appear.  Until the apparition happens, take care, and when a totally crazy man wins the mega-lottery and becomes unimaginably wealthy, should he then be considered merely eccentric?

Jim Muth
jimmuth@earthlink.net


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

On_the_Superspike  { ; time=0:00:20.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=cos
  center-mag=-4.185306304415169/+6.636739950187376/\
  7253877/1/58.75/0 params=1.333/0/1/0 float=y
  maxiter=2500 inside=0 logmap=41 periodicity=6
  colors=00000400500700810920A30A10B30C50D81AB27918C\
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  gImcFm`DrYArV8rS6rW6rZ6ma6me6mh6mk6mo6mr6Ou6Os7Oq8\
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  znGzpEziUzcizYyz_vzatzcrzepzgnzikzzizzgzzezzczzfzz\
  izzlzznzzqzztzzwzzyzzyzzyzzyzzyzzyzzezzMzz2zz5zz7z\
  zAzzCzzFzzHzzJzzMzzOzzRzzTzzVzzYzz`zzczzfzzizzlzzo\
  zzrzzuzzxzzvzzuzztzzrzzqzzpzznzzmzzlzzjzzizzhzzfzz\
  ezzdzzizzmzzrzzvzzzzzpzzf }

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=========================================