That is a surprisingly good result , the white regions of semi stability are where they are supposed to be and there occurrence is less with increasing values of p and h. The straight line along the lower portion of the image can be disregarded as this is most likely for zero values of h. There's some complexity within the main curve and one can zoom into that region , if desired. This type of curve might be quite different for other differential equations , however for now more exploration is required. I can now use my FreeBASIC fracmap1a.bas code to determine what sequences result and how stable they are. So the initial x,y values that you used were approx 0.73 and 0.73 ? On 21/11/2015 21:47, Hal Lane wrote:
Sciwise, In your request for me to calculate an image you didn't specify: - initial x & y values (for p1), or - a bailout value (p2)
so I'm arbitrarily using these values:
params=0.73899999999999999/0.73899999999999999/64/0
taken from the
parm file found in the original FreeBASIC.net
formula source post...
I turned *periodicity testing off* and used passes=1 for
image accuracy.
Your corner location X, Y specifications match the
X and Y
values calculated by Richard's Fractint 4 Win beta 5 from
the center-mag values in your parm file -- *after* using the
manually applied correction of: x-mag=0.75 *required* to compensate for a bug in Fractint for Windows beta 5.
Below is the final par file & formula I used to calculate your requested image -- using the additional info given above:
And the .GIF image it creates:
http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq0.gif [1]
Anti-aliased version:
http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq1.jpg [2]
Is
that what you were expecting to see, sciwise? hallane@earthlink.net
########################
-----Original Message----- From:
Fractint [mailto:fractint-bounces@mailman.xmission.com [3]] On Behalf Of
sciwise@ihug.co.nz [4] Sent: Friday, November 20, 2015 8:40 PM
To: Fractint and General Fractals Discussion
Subject: [Fractint] V-HeunPH a limited region
The images that you are generating from my simple formula. in the p , h plane are fascinating ; perhaps you can do a similar treatment using these parameters.
top left X 0.0025031289111390 y 0.8188647746243739
bottom right x 1.9949937421777222 y -0.6755031853255635
----- vhpp.par
test { reset=2004 type=formula
formulafile=fractint.frm
formulaname=V-HeunPH
center-mag=0.998748/0.0716808/1.338358 float=y
maxiter=2048
inside=bof61 outside=0 logmap=yes colors=@blues.map [6] }
--------- end par -------
I wasn't expecting the p , h plane ,to
be overly
complicated , however you can never tell when
fractals are involved.
The next step is to take the V-HeunPH values
and
use them with V-Heun.
Using the vhpp.par file we
obtaim a type of curve
that's at the boundary between the
unstable outside
and the ultra stable inside ; values from this
region
are what I may initially use for V-Huen , however
your explorations are suggesting other possibilities.
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