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 } --------- 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.
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 Anti-aliased version: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq1.jpg Is that what you were expecting to see, sciwise? <--<< ---------------------------------------------------------- VHeunS02 { ; Calc Request & parms fm sciwise. Nov 20, 2015 ; ; sciwise's Volterra Lotka formula (with modified ; initialization; and bailout repair used.) ; ; p, h are variable. ; ; frm - sciwise modified ver of 1993 V-Heun formula: "V-HeunPH", ; repaired, parameterized. ; reset=2004 type=formula formulafile=fractint.frm formulaname=V-HeunPH center-mag=0.998748/0.0716808/1.338358 float=y maxiter=2048 params=0.73899999999999999/0.73899999999999999/64/0 inside=bof61 outside=0 logmap=yes colors=@blues.map } frm:V-HeunPH { ; Sciwise's FRM REPAIRED BY RESTORING BAILOUT TEST -HHL x=real(p1) y=imag(p1) p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z|<=p2 } ---------- End of par file ---------------------- - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of sciwise@ihug.co.nz Sent: Friday, November 20, 2015 8:40 PM To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> 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 } --------- 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. _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus
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.
_______________________________________________
Fractint mailing list Fractint@mailman.xmission.com [7]
https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [8]
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Links: ------ [1] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq0.gif [2] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq1.jpg [3] mailto:fractint-bounces@mailman.xmission.com [4] mailto:sciwise@ihug.co.nz [5] mailto:fractint@mailman.xmission.com [6] mailto:colors=@blues.map [7] mailto:Fractint@mailman.xmission.com [8] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [9] https://www.avast.com/antivirus
participants (2)
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Hal Lane -
sciwise＠ihug.co.nz