Fractal visionaries and enthusiasts:

Today's FOTD is late.  The reason -- FL and I took a day off on Saturday.

The image is another view of the strange rectangle in the Z^(2.003)+C Julia sets.  The rectangle itself, or what is left of it, appears as the narrow blue-edged horizontal slit near the center of the frame.

The image has been double rotated only +1 and -3 degrees from the true Julia orientation.  When the Julibrot is sliced this close to the Julia orientation, a small rotation makes a huge difference.

A careful examination of the image will reveal that its apparent top-bottom symmetry is 'almost', and not 'exact'.

The name "Rectangular Surroundings" simply describes the location of the scene.  The rating of a 7 is in all ways average, and implies average satisfaction on my part.

The four-dimensional geometry of the strange rectangle, of which there are actually an infinity, is so complex that the rectangle can appear as almost anything.  More of these unexpected and surprising rectangular distortions will be posted as upcoming FOTD's.

The calculation time is perhaps the best feature of the image.  Even when calculated with the rather complex SliceJulibrot4 formula, the image finishes in a fireball 35 seconds.  All complexities may be avoided by viewing the image on one of the web sites.

For some reason the latest mass murder has me more revved up than other similar disasters.  The loss of innocent lives is bad enough, but, IMO, the worn-out knee-jerk responses coming from the media outlets simply make things worse.  Only an idiot would believe we could solve the gun-violence problem by passing more gun control laws or by securing more guns to protect ourselves with, but from what I am hearing on TV and talk radio, the world must be filled with idiots.

I hear suggestions that we must keep guns out of the hands of dangerous people.  This is another good-sounding idea that ain't gonna work.  It is already illegal for convicted felons or seriously mentally disturbed people to possess firearms, but many mass-murderers have no criminal or psychotic background.  

How would we decide who among the rest of the 'normal' population might be dangerous and must therefore be banned from possessing firearms?  While searching the general population for the dangerous ones among us, we would need to avoid any perceived profiling that might offend a disadvantaged minority'.  And we would certainly not want any perceived invasion of privacy.

When Fractal Central was located back in Baltimore, I saw 'stop the killing' rallies organized and held on a monthly basis for at least 30 years.  Of course, the rallies merely 'preached to the choir', and accomplished nothing.  It was almost a joke when a drive-by shooting took place at one of the rallies.  Despite the rallies, the killings have continued at a rate of up to ten a week for over 30 years, and my sister reports from back at old FC, that they are still continuing.

What is the point of all my talk about things people already know?  I have no idea.  But I'll have much more to ruminate on in upcoming discussions, and maybe as time goes on, a point will emerge.

There is always an immediate point about weather however.  Heavy clouds covered Fractal Central most all day today, but it stayed dry and the temperature was a pleasant 75F 24C.  Late in the day some breaks in the clouds appeared, bringing hope of a brighter day to come tomorrow.  The fractal cats spent the day taking it easy, which is always easy for cats to do when the humans are away.

The day went pretty well for the humans also, who had a day of antiquing down in Adamstown, which is near Lancaster.  The next FOTD will be posted whenever it is ready.  Until that glorious moment arrives, take care, and everyone knows what is wrong with the world, but why does no one fix it?

Jim Muth
jimmuth@earthlink.net


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

Rect_Surroundings  { ; time=0:00:35.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0.00174958\
  /29.21843/1/90/0 params=90/91/87/90/-1.7435/0/0.00\
  0175/0.073883/2.003/0 float=y maxiter=3000 inside=0
  logmap=18 periodicity=6 sound=off
  colors=000ZPRZPQYPPXOPWNOVMNULMTKMSJLRJKQIJPHJNGIM\
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  zOmzNmzNmzMmzLmzLmzKmzJmz }

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