Fractal visionaries and enthusiasts: 

We have had our share of PI.  It's time to move on to the square root of 2.  Today's image shows a sample of what can happen when the formula Z^(sqrt(2))+C is iterated sqrt(2) levels up the hyperladder when no function is applied.

The first thing that happens is the parent fractal, which is a shapeless mass of large bays with a very long zig-zagging filament (main spike) extending north.  Today's scene lies near the point where this filament connects to one of the smaller bays.

The minibrot that lies at the center of today's image is even more shapeless than its parent, and to make things worse, it lies in a rather difficult area of the parent, where the very high maxiter makes the calculation go slow.  Luckily, the web sites can speed up the viewing considerably.

Considering all this, I rated the image at a 6-1/2, one-half point of which is a reward for the not-quite-successful coloring effort.

The name "Squarely Rooted" explains itself.

Lots of sun and a temperature of 84F 29C made today's conditions near ideal here at Fractal Central.  A few minor showers popped up in the afternoon around the area, but they stayed away from FC.  The fractal cats were unusually restless most of the day, leading me to suspect that an unwanted cat was prowling nearby.

The day of the humans was nothing at all like the day of the cats (or the night of the living dead).  It consisted mostly of totally routine stuff made only a little more interesting by unwarranted references to flesh-eating zombies.  The next FOTD will be posted when I consider it ready.  Until that uncertain time arrives, take care, and fight for truth in advertising.

Jim Muth
jimmuth@earthlink.net


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

Squarely_Rooted    { ; time=0:08:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=+0.4396111301623483/+1.590005669004912/\
  21703/1/17.5/0 params=1.4142135624/0/1.4142135624/0
  float=y maxiter=35000 inside=0 logmap=-753
  symmetry=none periodicity=6 mathtolerance=0.05/1
  colors=000KCTKDWKEYKF`KGcKHeMIgNJhPJiQKjRLkTLlUMnW\
  MoXNpYOq_Or`Ps_PrZNpWLlTJhQHdNGaKEYHCUEAQB8M97JBAL\
  CCMDENEGOFIPGLQINRKPSMRTOTUQWWSYXU_YWaZYc_`f`chafj\
  bilcmndmlcqkbtiavh`wf_xeZycYzbYz`Xz_WzZVzXUzWTzUSz\
  TSzRRzQQzOPzNOzLNzKMzJMzLLzNLzPKzRKzTKzUJzWJzYJz_I\
  zaIzcIzdHzfHzhHzjGzlGznGzoFzqFzsFzuEzwEzxEziMzWUzZ\
  WzaYzd_mgamjcmjcmjcmiccicciccicciccicTicSicSimRimR\
  imQimPimPimOimOimNimNimOjmPjmQjmQkmRkmSkmSlzTlzUlz\
  VmzVmzWmzXnzXnzYnzZozZoz_oz`pzapzapzbqzcqzcqzdrzer\
  zfrzfszgszhszhtzitzjtzjuzkuzluzmvzmvznvzowzowzpwzq\
  xzrxzrxzsyztyztyzuzzvzzvzzuyzuxzuwzuvzuvzuuzutztsz\
  trztrztqztpztoztnztnzsmzslzskzsjzszzszzszzszzrzzrz\
  zrzzrzzrzzrzzrzzrzzqzzqzzqzzqzzqzzqzzqzzqzzpzzpzzp\
  zzpzzpzzpzzpzzpzzozzozzozzozzozzozzozzozzpzzpzzqzz\
  qzzrzzrzzszzszzszztzztzzuzzuzzvzzvzzvzzuzzuzztzztz\
  zszzszzrzzrzzrzzqzzqzzpzz }

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