Fractal visionaries and enthusiasts:

I try to keep the FOTD on its regular daily schedule, but perfection seems to always elude me.  This time I became more concerned in formula writing than actually finding fractals, which occupied me most all day Saturday, resulting in another day with no FOTD.  (Hey, the world didn't end.)  Only one worthwhile new formula emerged however, and even that one is more a reworking of an older formula than an all-new one.

NEW FORMULA ALERT!

Yes, you read it right.  Today I am rolling out the MultiExp formula, which draws fractals with minibrots that can be morphed between quadratic and any other higher order.  And as long as the 'other' order is a whole number, the minibrots will have none of those annoying discontinuities that spoil fractals such as those created by an expression such as Z^(2.5)+C.

Unlike most of my formulas, with up to 10 variables, the MultiExp formula has only 2 parameters.  The real part sets the 'other' order; the imag part controls the degree of morphing.  When the imag part is set to zero, the fractal is a perfect Mandeloid of the 'other' order.  When it is increased, the fractal it draws gradually morphs into the Mandelbrot set.  When it is set to a negative value, the fractal morphs into a Mandelbrot set rotated 180 degrees.  A nuisance I have not yet worked out is that the entire fractal quickly increases in size as the imag parameter is increased.  (I corrected this deficiency, which appeared earlier in a similar formula, when I wrote the AllNewDivideBrot formula a couple years ago, but in doing so, I robbed the earlier formula of much of its potential.)

At first glance, the parent fractal of today's image is an oversized Mandelbrot set much too large to fit on the screen.  An out zoom is needed to bring it onto the screen.  Today's image lies in some order-7 debris still filling the inside of the large minibrot on the main stem.

I named it "Reverse Fractal" because the elements appear to be pointing in toward the central minibrot rather than radiating outward from it.  The rating of a 7-1/2 might have been higher if I had given the coloring a bit more time.

Perhaps the best feature of the image is its very fast calculation time of 45 seconds, which will leave little time for disappointment to build if the image lays an egg.

Today here at Fractal Central began with a snow shower and a temperature of 10F -12C.  The rest of the day brought lots of sun, but the temperature topped out at only a very chilly 25F -4C, which kept the fractal cats lurking around the radiators.  FL escaped the worst of the cold by spending the day with a friend back in Baltimore, where the temperature reached 36F +2C.

The next FOTD will be posted in 24 hours.  Until then, take care and maybe the universe was created by a great fractal.  And maybe one of these days I'll reveal my beliefs about religion, but today is not that day.

Jim Muth
jimmuth@earthlink.net


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

Reverse_Fractal    { ; time=0:00:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MultiExp function=recip passes=1
  center-mag=-17.657530419327/+0.063742372081/6e+007\
  /1/20/0 params=7/10 float=y maxiter=1500 inside=0
  logmap=50 periodicity=6
  colors=000f0Gf0Fe0Ee0Dd0Cd0Bc0Ac09b08b07b06Z05V04R\
  03N02K12G22C31841650561872B83D94GA5JB6MC7OD8RD9UDA\
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  4J34K44L54L54M64N74O84O84P94QA4RB4SC4SC4TD4UE4VF4V\
  F4WG4XH4YI4YI9WKEULISNNRORPQWNR`MTdKUiIWmHXkIWjIWh\
  IWgIWeIWdJVbJVaJV_JVZJVXJVWKUUKUTKURKUQKUOKUNLTLLT\
  KLTILTHLT3NQGLTTKWeIZsEbrHarK`rN_rPZqSYqVXqXXq_Wpb\
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  ZczWczTczQczNczKczHczMczQczVczZczcczgczdczacz_czXc\
  zVczSdzQczNczMczLczLmzLrzCczLwzQczVczZczcczgczlczr\
  czpcznczmczkczjczhczgczeczdczbczaczPczDczEczEczFcz\
  FczGczGczHczHczIczIczJczJczKczKczHczKczMczPczRczUc\
  zYczWczVczTczSczQczgczgcz }

frm:MultiExp   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
b=imag(p1)+0.00000000000000000001:
z=z*z*fn1(z^(a)+b)+c
|z| < 100000000 }

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