Fractal visionaries and enthusiasts:

Today there is some good news and some bad news.   The good news is that I will take steps to assure the unbroken continuity of the daily FOTD's.   I will put several images and discussions into a spare directory and hold them for use on the days when I lack the time to find a new image and write a new discussion.   The bad news is that it will take several days to create the backup supply of FOTD's.   As a result, today's FOTD will be the last until March 9th.

On the Fractint list, Tony Hanmer wrote:

>  In a formula such as MandelbrotMix4, are there 
>  enough midgets to make very tiny jumps from one 
>  to the next, such that each midget stays the same 
>  size and orientation but only its surrounding detail 
>  changes slightly?  This would lead to animations 
>  with a stable midget, which would be amazing to see.

The answer is yes.   The number of midgets that could be created with the MandelbtotMix4 formula is one of the higher infinities, and animations such as you describe would be fascinating to watch.   But making animations with the M-Mix4 formula raises problems.   When the parameters are changed, the detail around the midgets does indeed change.   And the size and orientation of the midgets remains nearly unchanged.   But the midgets jump around in a totally unpredictable manner, and are quickly lost beyond the edges of the screen.   As a result, it becomes necessary to track the midgets down, and when they are finally found, sometimes with much difficulty, it is nearly impossible to position them in exactly the same spot on the screen.   The resulting animations are jerky and very unpleasant to watch.

Not much need be said about today's image.   It is a scene in a remote valley in the northwest quadrant of the cubic Mandelbrot set.   The image has been running for the last hour while I have been busy at other tasks.   The rating of a 4 hardly makes the render time of over 1-1/4 hours worth the effort.   The overall value comes in at a nominal 5.

The image may be seen with much less effort by viewing it on Paul's FOTD web site at:But before going there, give Paul a chance to render and post the image.

The light rain on Thursday morning ended before noon, leading to a cloudy and mild afternoon.   Before venturing outdoors, the dynamic duo checked the temperature and found it was 52F 11C.   They decided this was acceptable, and spent several hours in the yard, nibbling the new grass.   This morning is starting with similar weather.   We shall see what the duo decides.

My decision is to attack the pile of work still before me, so until next time, which will not be until March 9th, take care, enjoy fractals while you have them, and be certain you will always have them.


Jim Muth
jamth@mindspring.com
jimmuth@aol.com

START 20.0 PAR-FORMULA FILE================================

Cubic_Mandelbrot   { ; time=1:16:36.22--SF5 on a P200
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  formulaname=MandelbrotCube passes=1
  center-mag=-0.25362329215568170/+1.276686610281370\
  00/2.409843e+009/1/2.49999017136973389/7.615552049\
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  inside=0 logmap=-4088 periodicity=10
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  mNzmQzmTzmWzmZzmazmczmXzmQzmJzmCzm6zm8zm9zmAzmCzmD\
  zmEzmGzmHzmIzmKzmLzmMzmMz }

frm:MandelbrotCube {; Jim Muth  real(c),imag(c)
z=p1, c=pixel+p2:
z=z*(sqr(z))+c,
|z| <= 16 }

END 20.0 PAR-FORMULA FILE==================================