June 26, 1997: The Vanished Butterflies June 25 June 27 1997 FOTD Home


Fractal visionaries:

Today's fractal looks like an object of some sort, but I just can't place what it is that the picture reminds me of.  One thing that immediately comes to mind is that wonderful series of "Circle Limit" drawings by M.C. Escher, where the objects increase to infinity as the limit of the circle is approached, almost as though they were imbedded in a space of constant negative curvature.  But if this is the case, today's fractal should have been called "Octagon Limit".

This fractal is a good example of the type of image I prefer -- one that subtly hints at something familiar without actually picturing it.  It is this hint of familiarity that turns people on to fractals, just as it does to art of all kinds.

There is no reason for people to be put off by the mathematical aspect of fractals.  One can appreciate a rainbow without an understanding of the laws of reflection and refraction.  One can also appreciate a fractal without understanding the complex math behind it.  In fact, I no longer bring up the topic of math unless I see that the person is actually interested in it.

The world around us is filled with fractal shapes.  It always has been filled with fractal shapes -- we simply did not recognize them before we discovered fractals.  When I see the mountains and clouds, I see fractals; when I see a leaf, I see a fractal network; when I see the Arctic ice cap photographed from a plane, I see a fractal pattern.  When I see a fractal on the screen, I see these physical things and much more.

Certainly some of those fractal patterns that remind us of nothing actually do have undiscovered physical counterparts, perhaps on other planets, perhaps yet undiscovered on our own.  And I never stop wondering the ultimate thought -- is the universe the greatest fractal of all?

Today's fractal may not be the greatest fractal of all, but it's an acceptable one.  After all, it's difficult to come up with the greatest fractal of all every day.  The image is that of an obscure slice of the (-Z)^1.1 mandeloid.  The finished image has been posted as always to a.b.p.f. and a.f.p.

For tomorrow -- who knows.  We'll just have to wait and see.

Jim Muth

START PAR FILE FOR 19.6====================================

TheVanishedButterf { ; time=0:00:19.56-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=ManMinusN-XZ passes=1 center-mag=+1.58\
  -60.0434214984606456/35.3825248139930579 inside=0
  params=0.75/0/1.1/0/1/0 float=y maxiter=500
  logmap=yes periodicity=10

frm:ManMinusN-XZ {
|z| <= 16 }

END PAR FILE FOR 19.6======================================