🚀 go-pugleaf

	I have discovered an intriguing phenomena involving a new fractal
formula that I have been playing with.  It produces a new type of Julia
for the Mandelbrot mapping. What is interesting is that the equation to
produce it is very unlike the mandelbot and I am suprised that there
is any correlation at all between the two. The relationship is undeniable
however and you can examime it for yourself by plugging the centre
coordinates of your favourite mandelbrot or julia into this new formula
and looking at the geometry produced. You will undoubtably recognize
the patterns of the original projected in this new eightfold rotational
symmetry. You won't see any minibrots, but the new structure is as unique
and distinct to the region of the mandelbrot as a fingerprint.

    The equation evolved out of my original series of inductive fractals
that I posted to the net several years back and more recently from
my HT and QUARTET fractal formula.
----------------------------------------------------------------------
 htjulia {
; A new mandelbrot julia type from Noel Giffin.
      z = pixel,zp1=zp2=(0,0),huge=1.0e32:
      temp = z
      z = z*z + zp2
      zp2 = zp1
      zp1 = p1/temp*temp, (|zp2| <= huge) && (|z| <= huge) }
----------------------------------------------------------------------
    You can see that it uses the element store and shift technique
to produce the delay that is characteristic of all my inductive fractals
but adopts the double escape bounds check and the inverted term that
evolved from the HT and QUARTET formulas.

    As with all these inductive types, avoid using periodicity checks
and boundary tracing methods.

    An interesting hybrid can be produced by mapping to the 1/pixel plane
as in the classic mandover mapping.  If you can play with the mapping
function and figure out how to map to a cylinder or a torus you could
make some very nice bracelets. Be careful of this inverted method.
Some julia's produced are larger than the range of numbers usable by
fractint. (+-32.00 on the real axis or close to it.)
-----------------------------------------------------------------------
 htjul_inv {
;
      z =1/pixel,zp1=zp2=(0,0),huge=1.0e32:
      temp = z
      z = z*z + zp2
      zp2 = zp1
      zp1 = p1/temp*temp, (|zp2| <= huge) && (|z| <= huge) }
-----------------------------------------------------------------------

    The whole series of inductive fractals that I developed is available
from URL="http://spanky.triumf.ca/pub/fractals/formulas/noel.frm"
These two aren't there yet though.

    Information on the Quartet fractal is available via:
URL="http://spanky.triumf.ca/www/quartet-info.html"

 Some example images from these formula are available at:

URL="http://spanky.triumf.ca/pub/fractals/images/new/elefants.gif" and
URL="http://spanky.triumf.ca/pub/fractals/images/new/htjulia2.gif" and
URL="http://spanky.triumf.ca/pub/fractals/images/new/hytex6.gif"

I would be interested in hearing your ideas on how this relationship
to the mandelbrot works. Mail your responses to Noel@triumf.ca
or submit for discussion to the usenet group where this was posted.
I have tried many simple variants on this theme and none of the
others map directly to the Mandelbrot like this one does. Curious?

    Cheers,
    Noel Giffin,
    Noel@triumf.ca