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1998-02-16
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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #112
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Tuesday, February 17 1998 Volume 01 : Number 112
----------------------------------------------------------------------
Date: Mon, 16 Feb 1998 16:13:42 -0800
From: Mark Christenson <mchris@hooked.net>
Subject: (fractint) "there he goes again..."
comment { 2/16/1998 Mark "Bud" Christenson
It occurred to me that it might be fun (or maybe sadistic?) to
add a couple of knobs to old (t)rusty gravijul. The parameters
aren't compatible, but the function triplets are the same and the
params are paired with the fn()s. Why three controls for amplitude
and only one for offset? I dunno, call it a bias... ;o)
I don't have any .pars yet, but I'm sure I will, probably too soon.
Bud
}
frm:gravijul-a { ; generalized r^(-2) by Mark "Bud" Christenson 2/16/98
; defaults: p1 = (1,0) p2 = (1,0) p3 = (1,0) p4 = (0,0) p5 = (4,0)
z = pixel:
v = fn1(z)
w = p1*(v*v)
z = p3*fn3(p2/fn2(w)) + p4
|z| < p5
}
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------------------------------
Date: Mon, 16 Feb 1998 19:31:45 -0500
From: Gedeon Peteri <gedeon@InfoAve.Net>
Subject: Re: (fractint) "there he goes again..."
Mark Christenson wrote:
> comment { 2/16/1998 Mark "Bud" Christenson
>
> It occurred to me that it might be fun (or maybe sadistic?) to
> add a couple of knobs to old (t)rusty gravijul. The parameters
> aren't compatible, but the function triplets are the same and the
> params are paired with the fn()s. Why three controls for amplitude
> and only one for offset? I dunno, call it a bias... ;o)
>
> I don't have any .pars yet, but I'm sure I will, probably too soon.
>
> Bud
> }
>
> frm:gravijul-a { ; generalized r^(-2) by Mark "Bud" Christenson 2/16/98
> ; defaults: p1 = (1,0) p2 = (1,0) p3 = (1,0) p4 = (0,0) p5 = (4,0)
> z = pixel:
> v = fn1(z)
> w = p1*(v*v)
> z = p3*fn3(p2/fn2(w)) + p4
> |z| < p5
> }
p4 and p5??? They don't show up on my t screen! Never did; p3 is tops. Have
I got a bad copy of Fractint?
Gedeon
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------------------------------
Date: Mon, 16 Feb 1998 19:43:15 -0500
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) Gravijul variation...
Hi All,
Here are 5 pars using a variant of gravijul + 4 new gravijul pars.
Enjoy!
- Sylvie
frm:gravijul-v1 { ; Variation on Mark Christenson's gravijul by Sylvie
Gallet
z =3D pixel^imag(p3) :
w =3D fn1(z)
z =3D fn3(p1/fn2(w*w)) + p2
|z| < p3
}
sg_gravijul-v1_01 { ; . t=3D 0:01:26=
=2E84
; Copyright Sylvie Gallet, Feb 04, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm
formulaname=3Dgravijul-v1 function=3Drecip/log/log passes=3D1
center-mag=3D0/0/0.6666667 params=3D-1/-3.14159265358979/-0.05/1/7/3
float=3Dy maxiter=3D511 inside=3D0 decomp=3D256
colors=3DulVumV<3>ytZzv_yv_<29>UupStqRrp<18>6CR5AQ5AN<5>945A32A43<7>AEA=
AFB\
BHCCJD<8>IYPJ_RJ`R<6>LhM<12>wt1<12>DVF<9>BI9BH8BH8<4>9D6<2>MG7QH8UI9YJA=
a\
LBeMCgODjQF<2>nVJ<3>vdByg8yh5yi3<15>yukyvnyvo<8>yyxzzzyxx<20>X8GV5DW6D<=
1\
2>fKMgLNgLN<27>tkV cyclerange=3D0/255
}
sg_gravijul-v1_02 { ; . t=3D 0:05:21=
=2E87
; Copyright Sylvie Gallet, Feb 05, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm
formulaname=3Dgravijul-v1 function=3Drecip/tanh/log passes=3D1
center-mag=3D1.53398/0.311156/18.57704
params=3D-0.5/-0.25/-1/0.225/9/2.5 float=3Dy maxiter=3D2045 inside=3D0
decomp=3D256
colors=3D0A5<13>KV2LX2NZ1P_1R`1<3>hj0<6>bg0ag0_f1<3>Wd1Vd1Tc2Rb2<16>0P5=
<7>\
IJ4KI4LI5<10>d9H<8>K36I24G13D01F02<7>`0C<26>zzm<4>ztPzrKyoJxlH<6>lN4jJ2=
i\
I2<11>X95W96V86U77T67V98XD9<11>zpN<7>Uia<13>EP7DO5CM3AK0BJ0CI0<13>U30<4=
>\
cEGeHJgJNiMQkOUmRXoU`<3>wcm<15>K0K<6>3IC0LA0L9<2>0N6
cyclerange=3D0/255
}
sg_gravijul-v1_03 { ; . t=3D 0:00:43=
=2E45
; Copyright Sylvie Gallet, Feb 05, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm
formulaname=3Dgravijul-v1 function=3Drecip/abs/log passes=3D1
center-mag=3D0/0/0.6942545 params=3D-1.5/0.3/0.5/-1/4/2.25 float=3Dy
maxiter=3D1023 inside=3D0 decomp=3D256
colors=3DA00H63<14>ZKA_LAaNA<2>dQAfSAgTAiVAkXA<3>rcAteAufBvgCwhD<16>zzz=
<6>\
SE7QD6OC6<12>Q29Q29Q19R0AR1AR2A<2>T3AT3AT3AT3AT3A<106>B34A43A54<6>AEAAF=
B\
BHCCJD<8>IYPJ_RJ`R<6>LhM<12>wt1<12>DVFDUEDSEB00<4>G52
}
sg_gravijul-v1_04 { ; . t=3D 0:03:40=
=2E58
; Copyright Sylvie Gallet, Feb 05, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm
formulaname=3Dgravijul-v1 function=3Drecip/sqrt/log passes=3D1
center-mag=3D-1.11022e-016/1.11022e-016/0.7848492/1/12.499
params=3D1/0/0.6/-0.5/4/2 float=3Dy maxiter=3D255 inside=3D0 decomp=3D2=
56
colors=3D000<141>0E90FA0FA1GB1GB<28>J_RJ`RJaQ<4>LgNLhMOiK<11>wt1<12>DVF=
DUE\
DSE<5>G52<15>ZKA_LAaNA<2>dQAfSAgTAiVAkXA<12>I72
}
sg_gravijul-v1_05 { ; . t=3D 0:29:30=
=2E08
; Copyright Sylvie Gallet, Feb 14, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm
formulaname=3Dgravijul-v1 function=3Datanh/atanh/atanh passes=3D1
center-mag=3D0/0/0.3876293 params=3D0.95/0/0.09/0/4/2 float=3Dy
maxiter=3D151 inside=3D0 outside=3Dsumm periodicity=3D0
colors=3D040_J9cKAhMB<4>nVJ<3>vdByg8yh5yi3<20>zzz<6>SE7<3>LA5<3>000000<=
2>9\
03<126>9848959B6<13>IYPJ_RJ`R<6>LhM<12>wt1<12>DVF<14>AB54C5<5>VI9
}
sg_gravijul_05 { ; . t=3D 0:16:07=
=2E07
; Copyright Sylvie Gallet, Feb 14, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm formulaname=3Dgra=
vijul
function=3Datanh/atanh/atanh passes=3D1
center-mag=3D2.22045e-016/0/0.7075342
params=3D0.85/0/0.07000000000000001/0/2.95/0 float=3Dy maxiter=3D151
inside=3D0 outside=3Dsumm periodicity=3D0
colors=3DU00nVJ<3>vdByg8yh5yi3<20>zzz<6>SE7QD6OC6<14>Q19R0AR1A<20>iNOjP=
PjQ\
PjRP<29>xtZyv_xv`<28>UupStqRrp<18>6CR5AQ5AN<5>945A32A43<7>AEAAFBBHCCJD<=
8\
>IYPJ_RJ`R<6>LhM<12>wt1<12>DVF<9>BI9BH8BH8<4>9D6<2>MG7QH8UI9YJAaLBeMCgO=
D\
jQFkSGlUI
}
sg_gravijul_06 { ; . t=3D 0:48:33=
=2E40
; Copyright Sylvie Gallet, Feb 14, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm formulaname=3Dgra=
vijul
function=3Datanh/atanh/atanh passes=3D1
center-mag=3D-0.508795/0.563438/2.201573/1/-82.5
params=3D0.97/0/0.1/0/5/0 float=3Dy maxiter=3D151 inside=3D0 outside=3D=
summ
periodicity=3D0
colors=3D000A75<5>AEAAFBBHCCJD<8>IYPJ_RJ`R<6>LhM<12>wt1sr2pp3<30>CM9AKA=
AKA\
<13>CIACIABIA<86>0AA0AA1BB<44>OmlPnmOkl<15>6CR5AQ5AN<5>945A32A43A64
}
sg_gravijul_07 { ; . t=3D 1:02:08=
=2E83
; Copyright Sylvie Gallet, Feb 15, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm formulaname=3Dgra=
vijul
function=3Datanh/atanh/atanh passes=3D1
center-mag=3D-1.06581e-014/8.88178e-015/0.08286928
params=3D1/0/0.1/0/5/0 float=3Dy maxiter=3D255 inside=3D0 outside=3Dsum=
m
periodicity=3D0
colors=3D000ARQ<26>OmlPnmOkl<15>6CR5AQ5AN<5>945A32A43<7>AEAAFBBHCCJD<8>=
IYP\
J_RJ`R<6>LhM<12>wt1sr2pp3<30>CM9AKAAKA<13>CIACIABIA<86>0AA0AA1BB<16>9QP=
}
sg_gravijul_08 { ; . t=3D 1:06:56=
=2E97
; Copyright Sylvie Gallet, Feb 15, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm formulaname=3Dgra=
vijul
function=3Datanh/atanh/recip passes=3D1
center-mag=3D1.25928/0/1.323938/1/-90
params=3D0.87/0/0.07000000000000001/0/3/0 float=3Dy maxiter=3D255 insid=
e=3D0
decomp=3D256 periodicity=3D0
colors=3D963<85>llimljmlknllomm<2>ppoqqprrqssrttsuutvvuwwv<11>wwgwwfwve=
vud\
<4>tqZtpYsoXsnVrmUrmT<24>dQ3cP2bO2<8>ZJ1YI1YH0YG0XG0<3>WD0WD3<5>U93T84T=
8\
4T84<5>Q55Q55Q55Q55P45<8>N33M33M33L22L22<7>J01I01I00H00H00<5>E00E00D00C=
0\
0<18>200100100100<9>852 cyclerange=3D0/255
}
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------------------------------
Date: Mon, 16 Feb 1998 16:59:59 -0800
From: Mark Christenson <mchris@hooked.net>
Subject: (fractint) "there he goes again..." thud
Sometimes I remind myself of Wiley Coyote.
Sorry about that last shot. I forgot I only had three params to
work with. I'll re-issue gravijul-a later using real-only params (split
p1, p2, p3).
Bud
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------------------------------
Date: Mon, 16 Feb 1998 17:52:27 -0800
From: Mark Christenson <mchris@hooked.net>
Subject: (fractint) frm: prefix
I just got a surprise. While trying to view Sylvie's latest, Fractint
choked. Told me it couldn't find/open the formula. Does v19.3 not
understand the "frm:" prefix? (v19.6 works fine)
Bud
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------------------------------
Date: Mon, 16 Feb 1998 21:36:39 -0500
From: "Jason Hine" <tumnus@together.net>
Subject: Re: (fractint) FEIGENBAUM's constant: HELP ME
Paul helpfully replied:
>The constant shows up as alimit. Mark the bifurcations r1, r2, r3, r4...
>
>Then (r3-r2)/(r2-r1) is not f, nor is (r4-r3)/(r3-r2), but the sequence
>a1 = (r3-r2)/(r2-r1), a2 = (r4-r3)/(r3-r2), a3 =... is a convergent
>sqeuence with limit f.
I know an 80+ yr. old professor who teaches a single lecture series at colorado
State University, entitled 'Recursive Algorithms'. That title is a cover-up for
the fact that all he talks about are fractals! Anyway, he gave a less technical
definition of the Feigenbaum Constant as "[the limit of] the ratio of the
diameters of the disks along the x-axis." Just thought I'd mention it...
Jason Hine
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------------------------------
Date: Mon, 16 Feb 1998 21:39:57 -0600
From: "Tim Wegner" <twegner@phoenix.net>
Subject: Re: (fractint) frm: prefix
Bud asked:
> I just got a surprise. While trying to view Sylvie's latest, Fractint
> choked. Told me it couldn't find/open the formula. Does v19.3 not
> understand the "frm:" prefix? (v19.6 works fine)
No, the frm: prefix is a feature new with 19.6.
You can asnwer this kind of question yourself by looking at the quite
detailed revision history under "What's New". That's what I did!
Tim
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------------------------------
Date: Mon, 16 Feb 1998 21:39:57 -0600
From: "Tim Wegner" <twegner@phoenix.net>
Subject: Re: (fractint) FEIGENBAUM's constant: HELP ME
Jason said:
> I know an 80+ yr. old professor who teaches a single lecture series at colorado
> State University, entitled 'Recursive Algorithms'. That title is a cover-up for
> the fact that all he talks about are fractals!
Yes, this fellow writes and calls me often. I have a soft spot in my
heart for him; he seems a rather extraordinary fellow. But I can't
honestly agree with him that fractals should be a required part of
the math curriculum, with my book as the text <g!>
Tim
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------------------------------
Date: Mon, 16 Feb 1998 21:52:48 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: (fractint) Still more Herman Rings (long)
Ok, this is it. One more variation on the Herman ring formula that Paul
D. started all this with. I'm not sure I got the critical points exactly
right, but hey, it's worth twice what you paid for it. :-)
comment { ; narrative copyright Kerry Mitchell 16feb98
Variations on Herman Rings
The below formulas are based on the following formula, which is
known to produce Herman rings:
f(z) = alpha * z^2 * (z-c) / (1-c*z).
This can be generalized to:
F(z) = alpha * z^n * g(z)^m, where
g(z) = (z-c) / (1-c*z).
For the case of n >= 2 and m=n-1, it is believed that F(z) will
generate higher order Herman rings. The present formulas treat
the general case, where m and n are independent.
For the Mandelbrot-type formulas, the critical points of F(z)
are readily determined by solving a quadratic equation. To
maintain continuity in the image, the selection of critical
must be changed depending on the parameter c. Otherwise, lines
of discontinuity appear. These lines are hyperbolic (plus the
imaginary axis), according to (real(c))^2 - (imag(c))^2 = r^2.
This value of r depends on the exponents n and m:
r = (n^2 + m^2) / (n - m)^2.
This adjustment of the critical point is made in the formula
initialization.
The parameter alpha can be selected in two ways, either using
cartesian or polar coordinates. The advantage to polar coordinates
is that entering an irrational rotation angle is easy; enter a
*rational* polar angle for alpha, and the rotation angle (which
involves a factor of pi) will be irrational.
Five formulas are included: 2 Mandelbrot types (cartesian and
polar), 2 Julia types (cartesian and polar), and 1 Mandelbrot
type where c is explicitly specified and alpha takes on the
pixel value. For the Mandelbrot types, the choice of critical
point (using either the positive or negative root of the
discriminant) is governed by the sign of real(p3).
}
for-jay { ; copyright Kerry Mitchell 16feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=hermanm_man-polar center-mag=-0.76637882\
451330240/0/8000 params=2/-1/1/1/1/0 float=y maxiter\
=256 inside=0 decomp=256 periodicity=0 colors=000<40\
>x00z00z00<40>zy0zz0zz1<39>zzxzzzzzz<40>1zz0zz0yz<39\
>02z00z00z<41>000 cyclerange=0/255
}
alpha-sample { ; copyright Kerry Mitchell 16feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=hermanm_alpha center-mag=-0.534251/6.319\
/1.212533 params=4/-5/0.33333333333333/0/1/0 float=y
maxiter=256 inside=0 decomp=256 periodicity=0 colors\
=222<45>wn9ypAypA<45>fMheLieLieLi<43>bOlbOlaPm`Pm<29\
>4pp2qq2qq<30>Q`iQ`iP_h<45>266 cyclerange=0/255
}
another-doily { ; copyright Kerry Mitchell 16feb98
reset=1960 type=formula formulafile=fractint.frm
formulaname=hermanm_jul-cart center-mag=2.71257/-3.2\
1503/0.127551 params=0.168453633/0.17634814/4/-4/0/1
float=y maxiter=256 inside=0 decomp=256 periodicity=0
colors=o_K<19>yiUyiVyjVyjWxkW<27>jyijyiiyjiyjhxk<27>\
WjyVjyViyUiyUhx<59>0GW0GV0FV0FU1EU<27>F0GF0GG0FG0FH1\
E<27>UF0VF0VG0WG0WH1<38>n_K cyclerange=0/255
}
frm:hermanm_jul-polar { ; Kerry Mitchell 16feb98
; p1 = Julia parameter
; real(p2) = z exponent (use integer >= 2; m=n-1)
; imag(p2) = g exponent (integers)
; real(p3) = alpha magnitude (try 1)
; imag(p3) = alpha polar angle (try integers)
; use decomp=256
; zero and infinity bailouts hardcoded to 1e-6, 1e6
; coloring speed hardcoded to 4
z=pixel, c=p1, iter=1, n=real(p2), m=imag(p2), nfac=2*n-1
maxr=1e6, minr=1/maxr, speed=4*pi/128
r=real(p3), t=imag(p3), alpha=r*(cos(t)+flip(sin(t)))
oln=1/log(n), fac=log(0.5*log(maxr))
:
g=(z-c)/(1-c*z), z=alpha*z^n*g^m
iter=iter+1, r=|z|
;
; orbit trap around 0
; renormalize iteration count via decomp angle
; set "iteration done" flag (iter=-1)
;
if (r<minr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
z=cos(angle)+flip(sin(angle))
iter=-1
end if
;
; orbit trap around infinity
; renormalize iteration count via decomp angle
; add pi to angle to separate from 0 orbit trap
; set "iteration done" flag (iter=-1)
;
if (r>maxr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
angle=angle+pi
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
}
frm:hermanm_jul-cart { ; Kerry Mitchell 16feb98
; p1 = Julia parameter
; real(p2) = z exponent (use integer >= 2; m=n-1)
; imag(p2) = g exponent (integers)
; p3 = alpha (go nuts)
; use decomp=256
; zero and infinity bailouts hardcoded to 1e-6, 1e6
; coloring speed hardcoded to 4
z=pixel, c=p1, iter=1, n=real(p2), m=imag(p2), nfac=2*n-1
maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=p3
oln=1/log(n), fac=log(0.5*log(maxr))
:
g=(z-c)/(1-c*z), z=alpha*z^n*g^m
iter=iter+1, r=|z|
;
; orbit trap around 0
; renormalize iteration count via decomp angle
; set "iteration done" flag (iter=-1)
;
if (r<minr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
z=cos(angle)+flip(sin(angle))
iter=-1
end if
;
; orbit trap around infinity
; renormalize iteration count via decomp angle
; add pi to angle to separate from 0 orbit trap
; set "iteration done" flag (iter=-1)
;
if (r>maxr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
angle=angle+pi
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
}
frm:hermanm_man-cart { ; Kerry Mitchell 16feb98
; real(p1) = z exponent (use integer >= 2; m=n-1)
; imag(p1) = g exponent (integers)
; p2 = alpha
; real(p3) = critical point selector (>0 for positive root)
; imag(p3) = unused (<0 for negative root)
; use decomp=256
; zero and infinity bailouts hardcoded to 1e-6, 1e6
; coloring speed hardcoded to 4
c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1
maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=p2
oln=1/log(n), fac=log(0.5*log(maxr))
c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1
hypden=sqr(n-m), hypfac=hypnum/hypden
if (real(p3)<0)
pn=-1
end if
if (real(c2)>hypfac)
pn=-pn
end if
if (imag(c)<0)
pn=-pn
end if
afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n
d=sqrt(bfac*bfac-4*afac*cfac)
z=(bfac+pn*d)/(2*afac)
:
g=(z-c)/(1-c*z), z=alpha*z^n*g^m
iter=iter+1, r=|z|
;
; orbit trap around 0
; renormalize iteration count via decomp angle
; set "iteration done" flag (iter=-1)
;
if (r<minr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
z=cos(angle)+flip(sin(angle))
iter=-1
end if
;
; orbit trap around infinity
; renormalize iteration count via decomp angle
; add pi to angle to separate from 0 orbit trap
; set "iteration done" flag (iter=-1)
;
if (r>maxr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
angle=angle+pi
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
}
frm:hermanm_man-polar { ; Kerry Mitchell 16feb98
; real(p1) = z exponent (use integer >= 2; m=n-1)
; imag(p1) = g exponent (integers)
; real(p2) = alpha magnitude (try 1)
; imag(p2) = alpha polar angle (try integers)
; real(p3) = critical point selector (>0 for positive root)
; imag(p3) = unused (<0 for negative root)
; use decomp=256
; zero and infinity bailouts hardcoded to 1e-6, 1e6
; coloring speed hardcoded to 4
c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1
maxr=1e6, minr=1/maxr, speed=4*pi/128
r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t)))
oln=1/log(n), fac=log(0.5*log(maxr))
c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1
hypden=sqr(n-m), hypfac=hypnum/hypden
if (real(p3)<0)
pn=-1
end if
if (real(c2)>hypfac)
pn=-pn
end if
if (imag(c)<0)
pn=-pn
end if
afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n
d=sqrt(bfac*bfac-4*afac*cfac)
z=(bfac+pn*d)/(2*afac)
:
g=(z-c)/(1-c*z), z=alpha*z^n*g^m
iter=iter+1, r=|z|
;
; orbit trap around 0
; renormalize iteration count via decomp angle
; set "iteration done" flag (iter=-1)
;
if (r<minr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
z=cos(angle)+flip(sin(angle))
iter=-1
end if
;
; orbit trap around infinity
; renormalize iteration count via decomp angle
; add pi to angle to separate from 0 orbit trap
; set "iteration done" flag (iter=-1)
;
if (r>maxr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
angle=angle+pi
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
}
frm:hermanm_alpha { ; Kerry Mitchell 16feb98
; real(p1) = z exponent (use integer >= 2; m=n-1)
; imag(p1) = g exponent (integers)
; p2 = c
; real(p3) = critical point selector (>0 for positive root)
; imag(p3) = unused (<0 for negative root)
; use decomp=256
; zero and infinity bailouts hardcoded to 1e-6, 1e6
; coloring speed hardcoded to 4
c=p2, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1
maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=pixel
oln=1/log(n), fac=log(0.5*log(maxr))
c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1
hypden=sqr(n-m), hypfac=hypnum/hypden
if (real(p3)<0)
pn=-1
end if
if (real(c2)>hypfac)
pn=-pn
end if
if (imag(c)<0)
pn=-pn
end if
afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n
d=sqrt(bfac*bfac-4*afac*cfac)
z=(bfac+pn*d)/(2*afac)
:
g=(z-c)/(1-c*z), z=alpha*z^n*g^m
iter=iter+1, r=|z|
;
; orbit trap around 0
; renormalize iteration count via decomp angle
; set "iteration done" flag (iter=-1)
;
if (r<minr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
z=cos(angle)+flip(sin(angle))
iter=-1
end if
;
; orbit trap around infinity
; renormalize iteration count via decomp angle
; add pi to angle to separate from 0 orbit trap
; set "iteration done" flag (iter=-1)
;
if (r>maxr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
angle=angle+pi
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
}
- -------------------------------------------------------------------------------
Kerry Mitchell
lkmitch@primenet.com
- -------------------------------------------------------------------------------
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Date: Mon, 16 Feb 1998 21:44:23 -0800
From: "Jay Hill" <ehill1@san.rr.com>
Subject: Re: (fractint) Still more Herman Rings (long)
Hi Kerry,
My collection of your posts is updated:
http://home.san.rr.com/jayrhill/MITCHELL.ZIP
I suppose the following refers to me. Very nice. And if
you don't mind me looking around again....
for-jay-2 { ; after Kerry Mitchell 16feb98
; zoom in by Jay Hill
; Thanks Kerry for the cool formula
reset=1960 type=formula formulafile=mhermanr.par
formulaname=hermanm_man-polar
center-mag=0.418519/0.324914/26.02603/1/-67.5 params=2/-1/1/1/1/0
float=y maxiter=256 inside=0 decomp=256 periodicity=0
colors=000<40>x00z00z00<40>zy0zz0zz1\
<39>zzxzzzzzz<40>1zz0zz0yz<39>02z00z\
00z<41>000 cyclerange=0/255
}
We'll have to see what Dr. J thinks about this.
http://home.san.rr.com/jayrhill/FotN/FotNindx.html
>
> for-jay { ; copyright Kerry Mitchell 16feb98
> reset=1960 type=formula formulafile=fractint.frm
> formulaname=hermanm_man-polar center-mag=-0.76637882\
> 451330240/0/8000 params=2/-1/1/1/1/0 float=y maxiter\
> =256 inside=0 decomp=256 periodicity=0 colors=000<40\
> >x00z00z00<40>zy0zz0zz1<39>zzxzzzzzz<40>1zz0zz0yz<39\
> >02z00z00z<41>000 cyclerange=0/255
> }
>
[...]
> Kerry Mitchell
> lkmitch@primenet.com
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Date: Tue, 17 Feb 1998 08:34:54 +0100
From: Thore Berntsen <berntsen@vbdas.no>
Subject: (fractint) Fractint Screen Saver - Version 1.50 released!
You can find it at :
http://home.sol.no/~thbernt/fintsave.htm
Thore Berntsen
Email : thbernt@online.no
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Date: Tue, 17 Feb 1998 07:25:03 -0500
From: Lee Skinner <LeeHSkinner@compuserve.com>
Subject: (fractint) Gravijul vari
Hi Sylvie
>> sg_gravijul_08 { ; .<<
A cluster of satellite dishes??
Lee
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Date: Tue, 17 Feb 1998 10:39:26 -0500
From: Dave Kolasa <dak2@psu.edu>
Subject: (fractint) OT: Mathematicians Getting Rich from Algorithms
There's an article in the online version of Forbes Magazine that deals with
the Israeli software algorithm export industry:
http://www.forbes.com/asp/redir.asp?/forbes/98/0223/6104046a.htm
They claim the computer age is going to make a lot of you math-heads rich!
I hope you remember to invite the rest of us to the occasional fractal fest
at your mountain top condo(s).
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------------------------------
Date: Tue, 17 Feb 1998 12:44:43 -0500
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) Gravijul vari
Hi Lee,
>> A cluster of satellite dishes??
What an imagination! :-)
Here are a couple more pars:
sg_gravijul_09 { ; . t=3D 0:00:57=
=2E01
; Copyright Sylvie Gallet, Feb 17, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dsg_gravj.par
formulaname=3Dgravijul function=3Drecip/abs/acosh passes=3D1
center-mag=3D-4.44089e-016/4.44089e-016/0.383432
params=3D-0.35/1.55/-2/0.03/2.3/0 float=3Dy maxiter=3D300 inside=3D0
decomp=3D256
colors=3D3N3<46>3N33N35N4<6>JSDMTFMTF<4>NWF<9>wwc<4>www<20>llikkhkkhkkh=
<29\
>aaZaaZaaZaaZaaZaaZ3N3<2>3N3WWT<5>eebffcffc<3>hheiifjjgjjhkkh<24>wwuwwu=
w\
wuwwuvvt<67>aaZ
}
sg_gravijul_10 { ; . t=3D 0:01:32=
=2E44
; Copyright Sylvie Gallet, Feb 17, 1998
; <sylvie_gallet@compuserve.com>
; t=3Dcalc time using a Pentium 166 at 1600 x 1200
reset=3D1960 type=3Dformula formulafile=3Dsg_gravj.par
formulaname=3Dgravijul function=3Dsqrt/abs/acosh passes=3D1
center-mag=3D-2.77556e-017/0.369621/3.975055
params=3D0/1.5/-2.2/-0.1/2/0 float=3Dy maxiter=3D300 inside=3D0 decomp=3D=
256
colors=3DYE0<21>M25L15K06K07<17>L0LM0MO2M<5>_EJaHIcKG<10>vk3xm2xm2xm1xm=
0<8\
>kZ0jX0iW0hU0fS0<9>UC0TA0TA0<29>F22F22F22F22F22<46>577577677<29>kR7mS6n=
U\
6<6>uj1wm0wn3<7>yvXyw`yxdzzhzyfzwc<10>teBtc8sa8<11>YE0
cyclerange=3D0/255
}
Cheers,
- Sylvie
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Date: Tue, 17 Feb 1998 13:52:45 -0500
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) Two-piece Jigsaw Puzzle
Hi Paul,
>> Here's a formula that produces Julia sets that I find fascinating.
Very impressive images!!!
Cheers,
- Sylvie
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Date: Tue, 17 Feb 1998 12:04:48 -0700
From: Rich Thomson <rthomson@ptc.com>
Subject: Re: (fractint) Lee's PNG Ima
In article <009C1E6D.12875E08.2651@triumf.ca> ,
NOEL_GIFFIN <noel@triumf.ca> writes:
>I'm fairly certain that the problem with viewing Lee's PNG files from h
>is new gallery stems from a fault at the Mt. Allison web server.
There is an easy way to find out if this is true (it isn't now;
although I don't know if the server has been changed since Noel sent
his message)
telnet fractal.mta.ca 80
Trying 138.73.1.68...
Connected to ren.mta.ca.
Escape character is '^]'.
HEAD
http://fractal.mta.ca/fractals/skinner/1024_png/c2821/12821000.png
HTTP/1.0
HTTP/1.1 200 OK
Date: Tue, 17 Feb 1998 19:06:39 GMT
Server: Apache/1.2.5
Last-Modified: Wed, 21 Jan 1998 22:35:30 GMT
ETag: "15df5044-48aa9-34c67832"
Content-Length: 297641
Accept-Ranges: bytes
Connection: close
Content-Type: image/png
Connection closed by foreign host.
Doesn't look like there are any problems with the server.
- --
Rich Thomson
rthomson@ptc.com
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Date: Tue, 17 Feb 1998 13:20:52 -0600
From: Carolyn <car34slmo@worldnet.att.net>
Subject: Re: (fractint) Lee's PNG Ima
I am a new member of this list and want to confess at the onset that I
have absolutely no knowledge of what you all are talking about. But I
love the graphics and enjoy going to the URLs that are published on the
list just to see the images. Again, I don't know if this applies to this
message or not, but I found this site a couple of weeks ago even before
I stumbled onto my first fractal page. If this has no reference to this
situation at all, I ask you to excuse my error. I am hoping that some of
the stuff I am reading on this list will rub off. I would love to be
able to create some of the images I see represented.
I again ask you to excuse me if I have misread this message.
Carolyn
http://www.cdrom.com/pub/png/pngapvw.html
"There are also PNG plug-ins
available for both Netscape and Microsoft Explorer, which I hope
somebody
here can tell us where we can find them on the net."
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Date: Tue, 17 Feb 1998 15:55:12 -0500
From: Hailman@Prepnet.ucc.on.ca
Subject: (fractint) Hi everybody.
I just joined the list, but I have been using Fractint since 1992, when I got
"Fractals for Windows".
- --
Robert Hailman,
publisher of "Your Weekly Smile"
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Date: Tue, 17 Feb 1998 16:51:51 -0500 (EST)
From: ao950@freenet.carleton.ca (Paul Derbyshire)
Subject: Re: (fractint) Crash!
>True. It's often more subtle than that. Once a slightly corrupted image
>is read back in, the program can sometimes continue generating a few lines
>- then BANG! It may be a variable in the extension blocks that gets
>corrupted!
That wouldn't explain the initial hang, which was on a straight image
generation from scratch.
- --
.*. Friendship, companionship, love, and having fun are the reasons for
-() < life. All else; sex, money, fame, etc.; are just to get/express these.
`*' Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com
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Date: Tue, 17 Feb 1998 16:38:04 -0500
From: Hailman@Prepnet.ucc.on.ca
Subject: (fractint) Fractal Formula
I made a fractal formula, but I don't have it on this computer, go figure. Well
anyways, I'm making a par file and I will put it up when its done. The formula
is called "HailmanZCZCos(C)".
- --
Robert Hailman,
publisher of "Your Weekly Smile"
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Date: Tue, 17 Feb 1998 17:32:48 -0500 (EST)
From: ao950@freenet.carleton.ca (Paul Derbyshire)
Subject: Re: (fractint) spanky fractal database ups and downs
> Well you can laugh or cry depending on your disposition
>but here is Spanky's configuration.
>
> Microvax 3400 running VAX/VMS v 5.5-2HW in 12 MBytes RAM
You're joking.
VMS.
Please, please tell me you're joking.
:-)
> I think it is a credit to all the people responsible for the
>above software packages that allow a computer that has the performance
>level of about an Intel 386 system to compete in today's internet. I
>think Dave Jones at OSU should be particularly hilighted. His server
>has to be one of the most robust and efficient servers ever designed.
>Too bad it's only for VMS.
Too bad indeed... gak.
ObFractint:
Herman ring formula Julias make good B&W images for laserjet printing.
If there's any lake, put it black and everything else white; or put the
upper helf of the palette white and the lower black (or vice versa).
Usually this results in a printable image.
- --
.*. Friendship, companionship, love, and having fun are the reasons for
-() < life. All else; sex, money, fame, etc.; are just to get/express these.
`*' Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com
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End of fractint-digest V1 #112
******************************