Fractal visionaries and enthusiasts:

Today I will NOT count to ten before posting.  I see there has been another massacre, this one in Colorado.  I feel truly sorry for those who have suffered.  But what really pisses me off is the blather coming from the pundits on TV.  On one side we have simple-minded liberals who claim that this latest massacre shows the need for another gun control law, as if 3,624 laws would solve the problem when 3,623 laws have done nothing.  On the other side we have equally simple-minded conservatives who claim that the massacre shows the need for more guns in circulation to protect we good-guys from such psychopathic killers as well as the everyday minor bad-guys.

In my opinion, both liberal and conservative views are asinine.  The problem is the culture of violence in which we live.  Isn't it puzzling that we shield our youngsters from movie scenes of people loving each other yet expose them to scenes of people slaughtering each other, and then express shock whenever the latest mass murder takes place?  Why not go all the way and give our children 'Joker' masks for Halloween, so they will start behaving like 'The Joker' character?

Enough said for today, but you'd better believe that I'll have far more to say in future FOTD blogs.

As for the fractal, I'm back with today's FOTD!  And right on time!  And I bring with me an image that rates an 8.  It's not the best image ever, but (at least IMO) it's an improvement over the past several days' efforts.

We return to the mysterious rectangle in several Julia sets of the Z^(2.003)+C Mandeloid.  The area in question is the area just east of the large minibrot on the divided main spike of the parent Mandeloid.  The exact coordinates of the rectangle are C=-1.7435,0.0; Z=0.000175,0.073883.  A magnitude around 75 shows the rectangle to best advantage.

Today's image is named "Stretched Rectangle".  The reason for the name is visible in the image.  To wreak a bit of havoc, I have not sliced the scene in the exact Julia orientation.  I have rotated the view one degree in four different directions, producimg an almost-rectangle that is no longer a rectangle.  It now looks like a rectangular hole sliced in a sheet of stretched rubber.  In addition, parallel bands of high-iteration chaos have appeared inside the warped rectangle.

The whole image shows that, near the Julia orientation, small rotations in the direction of the slice make huge differences in the image.  The reason for this situation lies in the peculiar four-dimensional geometry of the Julibrot, which, because of laziness, I will not try to describe right now.

The calculation time is an everyday 2-1/2 minutes, just about average for a fractal on today's average machine.  Of course, this calculation effort may be avoided entirely by visiting one of the web sites.

Heavy clouds and rain spoiled today here at Fractal Central for those with outdoor plans.  The temperature of 68F 20C was most un-midsummerish, making the fractal cats come to life and wonder why the seasons are changing so fast.  The humans took the rain in stride.  FL was pleased to see her garden getting a much needed drink.

The next in the apparently unending line of FOTD images will be posted before too long.  Until whenever that might be, take care, and did you ever get the feeling that space aliens from outer space might be secretly running the show here on earth from behind the scenes?  I realize that no sensible person would believe such a thing, but no sensible person would believe the claims of modern science, especially relativity and quantum mechanics, either.

(Final note: as unrealistic and simple-minded as it might be, I am for removing all guns from our society.  Does anyone know of a way it might be done?)

Jim Muth
jimmuth@earthlink.net


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

StretchedRectangle { ; time=0:02:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/100
  params=89/89/89/89/-1.7435/0/0.000175/0.073883/2.0\
  03/0 float=y maxiter=32767 inside=0
  logmap=56 periodicity=6
  colors=000ZPRZPQYPPXOPWNOVMNULMTKMSJLRJKQIJPHJNGIM\
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  zOUzNUzNUzMUzLUzLUzKUzJUz }

frm:SliceJulibrot4   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z^(real(p5))+c
  |z|< esc }

END PARAMETER FILE=========================================