Fractal visionaries and enthusiasts:  

Today's FOTD image lies in the parent fractal that results when the expression Z^(1.9)+C is iterated 19 levels up the complex logarithmic hyperspiral with no function applied.  (I chose the value of 19 whimsically.)  This parent resembles a distorted Mandelbrot set rotated so that its main spike points to the southeast and its East Valley lies on the northwest side of the main bay.  Today's scene lies in one of the curious square shaped areas of chaos on the southwest side of the valley.

The unusual donut-ring effect was created by rendering the image with the outside set to 'fmod' which draws the overlapping circles.  The name "Donut World" refers to these rings of fractal stuff.

The art rates an 8, which might be a bit exaggerated, since I doubt that the hasty color work is the best I could do, but the math rating of a 7 seems about right.

The calculation time of 2-1/4 minutes is near FOTD average.  The average amount of time may be saved by checking the finished image on one of the web sites.

For all who have an interest in such things, the weather here at Fractal Central was totally perfect today, with photoshop blue skies, brilliant sunshine, low humidity and a temperature of 84F 29C.  The fractal cats, living the indoor life, took the outdoor conditions in stride; the fractal humans passed the day spending more time outside than usual.

The next FOTD will be posted in either one, two or three days.  Until whenever, take care, and let's combine all the world's religions, average out all the beliefs, and see what we come up with.  The way it is now, there are so many different and conflicting religious beliefs that any thinking person, especially in our materialistic science-based culture, must wonder if there is any real truth at all behind the world's different religious teachings.  Such doubt could easily be the reason so many lash out in anger when their religious beliefs are questioned or denied.

Jim Muth
jimmuth@earthlink.net


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

Donut_World        { ; time=0:02:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=-0.249919982284546/+0.07730680874550416\
  /3.250118e+009/1/122.5/0 params=1.9/0/19/0 float=y
  maxiter=2400 inside=0 proximity=0.068
  outside=fmod periodicity=6
  colors=000jZfk`fkbgkdhlfjlimllpmosmrwmuzmxzlvzltzk\
  szkqzkpzjnvjmsjkoijlihliglhelhclgblg`lg_lfYlfXlfVl\
  eUldSlaSlZRlWRlURlUSoURlUQjUPgUOeUNbUM`ULYZMYXKWWJ\
  VVIUUHTTGRSFQQDPPCOOBMNALM9KL8JK7IL6KM6LM6NN6OO6QO\
  6RP5TQ5UQ5WR5XS5ZS5_T4aU4bU4dV4eW4gY2pX3lW4hV5eU6a\
  T7YS8VR9RQANPBKOCGNDCI70LA5ND9PGDRIHTLLVOPXQTZTY`W\
  abZed`ifcmhfqjhuPNmRPkSQjTSiUThVUgWWfXXeYZcZ_b_`aa\
  b`bc_cdZdfYegWfiVgjUhkTimSjnRrpRnoQkoQhoQdoPaoPZoP\
  VnOSnOPnOLnNInNFnN7pHCnNGlSKjXOhaSffWdk_bpcbwc`ucZ\
  scYrcWpcVncTmcSkcQicPhcNfcMdcKccJacH_cGZcEXcDVcBUc\
  ASc8Qc7Pb9QbBQbDQbFQbHRbJRbLRbNRWXOZUP`RQbORdLSfIT\
  hFUjCVl9Wn6Xs4Xp3Ym3Zj3_h3`e3ab3a`3bY3cV2dT2eQ2eN2\
  fL2gI2hF2iC0kD2iE3hE4fF5eG7cG8bH9`HA_ICYJDXJEVKFUL\
  HSLIRMJPMKONMMONLOOJPPIQRGQSFRTDRW6RUCSSHTQNUPSTNY\
  SLbRLpQKkPKgOJcNJ_MIWLISKINJHJIHKHGLGGMFGNEGODGPCI\
  QBKRAMS9PT8RU7TV6UW5VX4WY }

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