Fractal of the Day
by Jim Muth

The Mighty Oak Tree ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- November 10, 1999

Fractal enthusiasts and visionaries:

Mighty oaks from tiny acorns grow, and mighty fractals from mighty oaks grow.   There's not much question of why I named today's fractal offering "The Mighty Oak Tree".   It's a tree -- plain and simple.   But there could be some question as to why I chose an oak tree.

I chose this particular tree because oak trees are the largest and most common trees in the Fractal Central area.   If I were in Australia, I might have chosen a eucalyptus tree, or if I were in Arizona, I could have chosen a cactus.   These are both mighty plants, but I looked out the window and saw an oak tree, so an oak tree it is.

The image is another venture into the the Julia planes of the formula (-Z)^1.05+C.   The Julibrot of this formula is boring only when it is sliced down the center.   Off to the sides, (all eight of them), it's filled with detail of the most unusual kind.

The other five sets of planes are also interesting.   I've already written the formulas to explore these other planes as well as the oblique planes.   Some of the things I find there will appear as the FOTD in the days to come.

The parameter file runs in about two minutes on a Pentium -- just about the time it will take to download the JPEG image file from:or from:
While browsing this afternoon, I noticed a used computer for sale -- a Pentium 200mhz at a ridiculous price.   Tomorrow, I might take a copy of Fractint and test the machine for speed and compatibility.   If all goes well, I'll buy it and dedicate it to calculating fractals.   This means that we might be seeing a lot more of those slow, slow images before long.

Meanwhile, the fractal weather was just about perfect today, with bright sun and a temperature of 70F (21C) shifting the fractal cats into stretch-out mode.

It was a bit warm for the most intense kind of pondering, but I managed to do a modicum of it at intervals during the course of the day.   The topic of my thought was the question of free will -- do we have free will or is everything predestined?

Our nature revolts against the slavery of a predestined world in which we are but as puppets moved by strings.   If we accept such a determinism, there seems to be no reason why we should ever attempt to live nobly.   Since everything is already determined anyhow, and we cannot escape from our preordained fates, we might as well relax, abandon all struggle and effort, and descend to the level of an animal existence.   Surely, a world where we are free is preferrable to one where we must act out the things that already exist.   And if one has no choice but to be as he is, what then of evil and punishment or of goodness and reward?

It might not be this bleak.   On the surface at least, it would seem apparent that yes, within our physical limitations and the legal constraints of society, we do indeed have free will.   This can easily be demonstrated.   At this moment I am free to either raise my right arm or keep it on the desk.   (I have just decided to keep it on the desk, but if I had decided to raise it, I would have had the freedom to do so.)

So far, so good, but what if my decision were based upon the toss of a coin?   What if it were based upon a particular firing of neurons in my brain?   Would I have had the freedom to do something other than that caused by the firing of my neurons?

At the everyday level, the physical world is one of cause and effect, cause always preceding effect, effect always following cause.   My decision was in fact caused by the particular order in which the neurons fired.   And that firing order was caused by a certain input of my senses, mixed with the effects of a previous firing which represented my thoughts leading to the decision.

This cause and effect train can be regressed indefinitely.   My decision was caused by a line of events that perhaps extends back to the creation of the universe.   And even more ominous, the causes presently active in the world might have already determined the future, and nothing anyone can do could possibly alter that predetermined future.   In its ultimate form, this line of thought leads to Calvinism.   (If God knows that I will go to hell, what is the use of trying to be good?)

I've got much more to say along the free will line, but for today I'm out of time and energy.

For now, I see it's time to check the fractal cats and call it a day.   Until tomorrow, take care, and we always have the free will to search for and find fractals.


Jim Muth
jamth@mindspring.com

START FORMULA==============================================

JuliaMiN {; Jim Muth
b=p1, z=pixel+p2, c=p3:
z=(-z)^(b)+c,
|z| <= 16
}

END FORMULA================================================

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

The_Mighty_OakTree { ; time=0:02:14.84 on a p233, SF5
  reset=2000 type=formula formulafile=slices.frm
  formulaname=JuliaMiN passes=1
  center-mag=1.75919/-1.38778e-017/6.564424/1/90
  params=1.05/0/0/0/3.5/0 float=y maxiter=1200
  bailout=25 inside=0 logmap=73 symmetry=none
  periodicity=10
  colors=000KOOOPOMNN<2>HMKFMJELICKH<2>7IE6HD4IC3IB<8\
  >TfcWifZlj<3>ivv<3>WZySTzPOz<3>Aez7jz3nz0rz<3>8gzAd\
  zCazD_z<3>CdzBezBfzBgzBhz<7>KbzLazMazN`zO_zP_z<9>eH\
  zfFzhDz<3>n6z<3>hGzgJzeLzdOzcQz<3>hKziJzjIz<3>nDz<3\
  >a8zZ7zW6zrPz<3>KOzCOzFLz<3>QCzTAzV7z<2>b1z<3>kIznM\
  zpQz<2>vaz<4>OXzHWzBVz<3>Waz`bzedz<2>thz<3>jVzhSzfO\
  z<3>YBz<4>iJzlKznMz<3>wRz<3>j`zfczcez<2>Vlz<5>cdzdc\
  zfbz<3>kYz_Xzj`z<3>jKzTfz<3>96z<5>6Fz5Gz5Iz<3>3Nz<3\
  >SMzYMzcMz<2>uMz<3>ZAz<4>PKzNLz<3>SNzUNzVOzWOzXOz<1\
  0>PCz
  }

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

START 19.6 PAR-FORMULA FILE================================

The_Mighty_OakTree { ; time=0:02:14.84 on a p233, SF5
  reset=2000 type=formula formulafile=slices.frm
  formulaname=JuliaMiN passes=1
  center-mag=1.75919/-1.38778e-017/6.564424/1/90
  params=1.05/0/0/0/3.5/0 float=y maxiter=1200
  bailout=25 inside=0 logmap=73 symmetry=none
  periodicity=10
  colors=000KOOOPOMNN<2>HMKFMJELICKH<2>7IE6HD4IC3IB<8\
  >TfcWifZlj<3>ivv<3>WZySTzPOz<3>Aez7jz3nz0rz<3>8gzAd\
  zCazD_z<3>CdzBezBfzBgzBhz<7>KbzLazMazN`zO_zP_z<9>eH\
  zfFzhDz<3>n6z<3>hGzgJzeLzdOzcQz<3>hKziJzjIz<3>nDz<3\
  >a8zZ7zW6zrPz<3>KOzCOzFLz<3>QCzTAzV7z<2>b1z<3>kIznM\
  zpQz<2>vaz<4>OXzHWzBVz<3>Waz`bzedz<2>thz<3>jVzhSzfO\
  z<3>YBz<4>iJzlKznMz<3>wRz<3>j`zfczcez<2>Vlz<5>cdzdc\
  zfbz<3>kYz_Xzj`z<3>jKzTfz<3>96z<5>6Fz5Gz5Iz<3>3Nz<3\
  >SMzYMzcMz<2>uMz<3>ZAz<4>PKzNLz<3>SNzUNzVOzWOzXOz<1\
  0>PCz
  }

frm:JuliaMiN {; Jim Muth
b=p1, z=pixel+p2, c=p3:
z=(-z)^(b)+c,
|z| <= 16
}

END 19.6 PAR-FORMULA FILE==================================




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