🚀 go-pugleaf

	I'm posting another image to the a.b.p.f. newsgroup and as I know that
some of you don't receive the alt hierarchy or follow the pictures newsgroup,
I thought I would include the header file here as I think this fractal is
quite significant and some of you may be interested in the developments.
==========================================================================
The header
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	This image shows some of the variations in fractal structure found
within the quartet fractal. This is a similar region to the one that made
the quartet1 and the scarab2 fractals posted several weeks ago but the result
is again quite different. 

   The two are similar in some aspects. If I understand it correctly, while
being more beautiful, they are similar to the Sierapinski gasket in that the
fractal produced has a perimeter but no area. Well at least not at the points
I have shown here.  It is possible to select a parameter value where large
areas will always  iterate to the maximum, but I find it more interesting to
find values of the P1 parameter where the fractal would seemingly iterate to
point infinitys. These would seem to have no true area.

	The two are similar in some aspects. If I understand it correctly
they are similar to the Sierapinski gasket in that the fractal produced has 
a perimeter but no area. Well at least not at the points I have shown here. 
It is possible to select a parameter value where large areas will always 
iterate to the maximum, but I find it more interesting to find values of
the P1 parameter where the fractal would seemingly iterate to point infinitys.
These would seem to have no true area.

    The set is not globally connected. It is clear that the top half
is disconnected from the bottom half, but what is not shown here clearly is
that the top section here is linked to the bottom half of the adjacent section
to the left. The whole infinite series interlocks like a chain.

	The major factor in controling the structure is the choice of the real 
and imaginary components of the P1 parameter. Originally I thought the only
interesting point was where the real component approached zero and the
imaginary component was even smaller or zero. Now I find that there are many
points where extreme fractal detail can be induced. It is easy to find one.
There are critical values where the structure changes drastically and large
areas will go to the maximum iteration value. Take a substantial increment in
a positive direction to make the structure shift back to make these| Forwar
areas shrink to a point and then take smaller step increments approaching the
critical value, increasing the iteration limit until a reasonable detail is
achieved.


	The formula again
======================

quartet = {
; The quatro-HT variation. Use real part of 0.0 < p1 < 1.0
; Adding the inversion causes what looks like an infinite extension along
; the real axis. Using the Imag component will add some nice asymmetry.
;
       z=pixel, zp = (0,0), huge=1.0e32:
       temp = z
       z = sin(z) - zp
       zp = p1/temp,(|zp| <= 4 &&|z| <=huge) }