Fractal visionaries and enthusiasts:

The minibrots in some fractals are connected to the main body of the larger fractal in which they exist.  The minibrots surrounding the Mandelbrot set are all connected by thin filaments to the main body of the M-set in this manner.  Other minibrots have no connection to the rest of their fractal, and exist as island universes, scattered around the fractal's main body like moons frozen in time.

Today's FOTD image shows one of these disconnected minibrots.  The parent fractal is a tiny Mandelbrot set surrounded by a cloud of minibrots, which in turn are surrounded by smaller clouds of minibrots, etc, etc., all the way down.  The image shows a minibrot near a larger minibrot in one of these sub-clouds.

Since the larger minibrot is itself disconnected, the pattern surrounding the minibrot in today's image consists of disconnected patches, filled with still smaller clouds of minibrots, all of which are well beyond resolution.

In my fractals, I usually try to avoid overly busy and brilliant colors, but in today's image the excessively gaudy color palette actually seems to improve the overall appearance.  If I had had more time, I might have gotten a bit more action from the underlying iteration bands, but even as the image is, it earns its place as FOTD for April 02.

The name "An Island Universe" tells it like it is.  The image is part of an island, and it has a universe within its depths.  The rating of a 7 is becoming so common that the FOTD rating system is starting to become redundant.

The calculation time of a fireball 18 seconds seems too good to be true, but take my word, the image calculates in just that time.

Another way to see the image is to view it in finished form on the currently active FOTD web site at:

http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html

The venerable original FOTD web site is still available at:

      http://www.Nahee.com/FOTD/

My own web site is almost ready.  All I want to do is prepare a proper home page with a brief introduction to the world of fractals.  I have also decided to include a gallery of several hundred images that I saved to disks in the years before I began the FOTD.  These old images, which go back to the late 1980's, were created with various fractal programs.  Most have no parameter information embedded.  They are not up to current standards, but they are still interesting images, showing how I launched my fractal explorations.

Friday here at Fractal Central began with wet snow that melted as it fell.  By midday the snow had changed to rain, which slacked off to sprinkles in mid-afternoon and ended by sunset.  The temperature reached a chilly high of 43F +6C, keeping the fractal cats within leaping distance of the heat.

The rest of the day was filled with routine everyday stuff such as making money.  The next FOTD will likely be posted in 24 hours.  Until then, take care, and if you know what a lemac is, you're probably not a teen-ager.

Jim Muth
jamth@mindspring.com


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

An_Island_Universe { ; time=0:00:18.56-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident float=y
  center-mag=-4.027874401682518/+0.4760310157376794/\
  2.0925e+11/1/117.5/0 params=3/0.75/0.8/-3.3/0/0/0/0
  maxiter=1500 inside=0 logmap=67 mathtolerance=/1
  colors=000UOUURcKSWSVMOdUrmmeVLSJEEC7zU6jM4QF3D71p\
  4kKxGFhCAU85F4aTXIkK44f33h22T1104zQz04aC3P82C41zz0\
  gONTGFE87ec`SQOEDCJbQCQH6D8`_AII5CW68L44N2agCTXALO\
  8891abvPQbCDJWCXO9OG6G838Ad65K3kGiO8NpKIbFDQA9D543\
  Hw18UqtK_aDIJ6455_AwyA`d6OK3Cf8qS5_E2I5jUPQiCDNeIR\
  m2Qos8be6QS4DE2L6KY0`P0RH0I809SujIaV9JFv4dT2KEp_7Q\
  IPWgCGMNeuBLTB`M7OE3C73iu2Yf1NT0BEnfMYSEHE7A_l7R_5\
  IO29CnNbPBJOEiG9U84FUyNMiHFVB7F5fCJW9EOYcSccYhbXic\
  WicWicVjcVjcUjcUjcTkcTkcSkcSlcRlcRlcQlcQmcPmcPmcOm\
  cOncNncNncMocMocLocLocKpcKpcJpcJpcIqcIqcHqcHrcGrcG\
  rcFrcFscEscUscUscUtcUtcUtcUucUucUuccuccvccvccvccub\
  cvccvccvcmvcmvcmvcmvcmvcmwcmwcmwcmwcmwcmwcmwdmwdmx\
  dmxdmxdmxdmxdzxdzxdzxdzxdzydzydzydzyezyezyezyezyez\
  zezzezzezzezzezzezzezzezzezxdzzdzzdzzdzzdzzdzzczzc\
  zzczzczzczzczzczzbzzbzzbzzbzzbzzbzzazzazzazzazzazz\
  azzazz`zz`zz`zz`zz`zz`zz_ }

frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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