Fractal of the Day
by Jim Muth

A Fractal Orchard
Jim Muth's fractal image in GIF format (640x480).


FOTD -- February 26, 1999

Fractal enthusiasts:

The weather today was cloudy and cold with flurries of snow.   The temperature of 32F 0C was chilly enough to keep both cats and people inside the fractal shoppe, the cats curled by the radiator, the person hunched over the computer.

The person in the fractal shoppe, who just happened to be me, produced a peachy little fractal for today.   So peachy is the image, in fact, that I have named it "A Fractal Orchard".   It is a fractal peach orchard of course.   I gave it this name because after gazing at the picture for a couple minutes, trying to think of a name, a sudden overwhelming desire for a dish of peach ice cream came over me, leaving me no choice but to rush to the freezer -- and all this with such a chill in the air.   As I ate my ice cream, dripping a sizeable chunk onto the keyboard, I decided on the name for the fractal.   Then I cleaned the keyboard.

Actually, the image is part of one of those 'magnified difference' fractals that I have grown so fond of these past few weeks.   In this case, I magnified the difference between Z^0.4 and Z^0.404 by a factor of 370 before adding C.

This MandelbrotMix4 formula is the richest I have yet devised, and a great part of its worth lies in its simplicity.   It contains no plethora of lines defining the color scheme.   When I use it, I rarely utilize more than Fractint's most basic coloring methods.

Everything in today's picture is the work of the numbers.   Every tiny peach-colored spot is in its exact position because it could be no other way.   This is why I frown upon involved coloring schemes -- they create lovely images, but they hide the things the numbers are doing.   And to observe what the numbers are doing is for me most of the fun of fractal exploration.

Today's picture has been posted in old-tyme GIF format to:and to Paul Lee's site on the WWW at:
It's now time to close Fractal Central for another day, but the shoppe will open again tomorrow at this same time with another glorious fractal to inspire awe and wonder.   In addition to a fractal, it is quite likely I'll have another spate of fractosophy.   A number of interesting messages were posted to the Philofractal list earlier today, and those messages need a reply.

So until next time, take care, but don't take so much care that you miss the fun in life.


Jim Muth
jamth@mindspring.com

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

MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f,
h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1,
l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

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

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

A_Fractal_Orchard  { ; 1/2hr on a 486-100, 640x480
  reset=1960 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+1.37965506012733400/+0.00013289366118996\
  /1.646902e+012/1.0001/15.008/-0.013
  params=-1/0.4/1/0.404/370/0 float=y maxiter=1600
  bailout=25 inside=0 logmap=96 symmetry=xaxis
  periodicity=10 colors=000GRX<17>Gmi<18>4E7<10>zadzcd\
  ze`zg_xhYxkWwnVwmTvpSvZQ<10>rW8rW7pX9<22>Tbf<4>dVmbM\
  fePhhSj3QC<4>dVe94hMDiZMjx3_<2>nOhmuUloYloakidkih9ld\
  JnfTqhbrjsuz<4>lvm6vu<5>exlexy<5>kym2zF<4>dzfwzO<6>l\
  zhxzLqzZLziUzjbzk8zj<6>fzk8zm<2>azkKzU<5>dzghzimzE\
  <6>kzgXzL<6>jzh3zYIzbXzgVzn<6>izkkzp<4>kzkjzZ4zCQzUD\
  z`<6>gzjbza<6>jzjdz32zYPzdVzdczhGzC<6>gzgPza<2>fzi\
  GzVGzWGzX
  }

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

START 19.6 PARAMETER-FORMULA FILE=========================

A_Fractal_Orchard  { ; 1/2hr on a 486-100, 640x480
  reset=1960 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+1.37965506012733400/+0.00013289366118996\
  /1.646902e+012/1.0001/15.008/-0.013
  params=-1/0.4/1/0.404/370/0 float=y maxiter=1600
  bailout=25 inside=0 logmap=96 symmetry=xaxis
  periodicity=10 colors=000GRX<17>Gmi<18>4E7<10>zadzcd\
  ze`zg_xhYxkWwnVwmTvpSvZQ<10>rW8rW7pX9<22>Tbf<4>dVmbM\
  fePhhSj3QC<4>dVe94hMDiZMjx3_<2>nOhmuUloYloakidkih9ld\
  JnfTqhbrjsuz<4>lvm6vu<5>exlexy<5>kym2zF<4>dzfwzO<6>l\
  zhxzLqzZLziUzjbzk8zj<6>fzk8zm<2>azkKzU<5>dzghzimzE\
  <6>kzgXzL<6>jzh3zYIzbXzgVzn<6>izkkzp<4>kzkjzZ4zCQzUD\
  z`<6>gzjbza<6>jzjdz32zYPzdVzdczhGzC<6>gzgPza<2>fzi\
  GzVGzWGzX
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f,
h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1,
l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 19.6 PARAMETER-FORMULA FILE===========================



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