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1998-11-14
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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #332
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Sunday, November 15 1998 Volume 01 : Number 332
----------------------------------------------------------------------
Date: Fri, 13 Nov 1998 23:28:54 -0500
From: JoWeber <JoWeber@compuserve.com>
Subject: (fractint) My Dog Ate the Internet!
Hi Paul,
>>Sylvie Gallet posted something called "ifs". I copied them, but don't
know how to view them - I keep getting an error message. Any tips? =
=
Edit the file, copy all ifs-formulas into a file with the suffix .ifs,
start fractint and let it calculate the pars.
BTW Wonderful images.
Cheers --Jo--
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------------------------------
Date: Sat, 14 Nov 1998 18:15:30 -0500
From: Paul DeCelle <PaulDC@prodigy.net>
Subject: Re: (fractint) .ifs files
> JoWeber wrote:
> Edit the file, copy all ifs-formulas into a file with the suffix .ifs,
> start fractint and let it calculate the pars.
Thanks, Jo - I'll give it a try.
Regards, Paul DeCelle
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------------------------------
Date: Sun, 15 Nov 1998 02:11:57 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: (fractint) New goodies
I've updated my collections of Fractint and UltraFractal coloring schemes.
The new toys are both "curve"-type colorings: color by closest approach
to a curve or how often the orbit is inside the curve. The curves are:
general polar curves where r is a function of theta, and the astroid curve
(4-pointed star or hypocycloid). I'll be posting the actual formulae and
parameters files to each list shortly. Until then, you can find the
updated files at:
www.primenet.com/~lkmitch/lkm-pub.zip
for Fractint stuff, and
www.primenet.com/~lkmitch/lkm-pub-uf.zip
for UltraFractal stuff.
Enjoy,
Kerry
- -------------------------------------------------------------------------------
Kerry Mitchell
lkmitch@primenet.com www.primenet.com/~lkmitch/
- -------------------------------------------------------------------------------
- --------------------------------------------------------------
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------------------------------
Date: Sun, 15 Nov 1998 07:40:23 -0500
From: davides <davides@pipeline.com>
Subject: (fractint) Inverse Julias
Below are some inverse julias. They take a little while to complete:
=========================++++++++++++============================
An_Inverse_Julia { ; (c) David Shanholtzer Nov 14, 1998 t=0:19:13.27
; P200 MMX 1024x768
; color map: dav86
reset=1960 type=julia_inverse miim=depth/right
center-mag=0/0/0.6666667 params=-0.0197/0.71/235 float=y
maxiter=10000 inside=zmag
colors=000ZBZ<52>zzz00U<60>xxyzzzzzz<62>00Uzzz<60>V2VU0UU0U<9>ZAZ
}
An_Inverse_Julia1 { ; (c) David Shanholtzer Nov 14, 1998 t=0:20:37.58
; P200 MMX 1024x768
; color map: Dav86
reset=1960 type=julia_inverse miim=depth/right
center-mag=0/0/0.6666667 params=-0.012/0.6556999999999999/235
float=y maxiter=750000
colors=000ZBZ<52>zzz00U<60>xxyzzzzzz<62>00Uzzz<60>V2VU0UU0U<9>ZAZ
}
An_Inverse_Julia2 { ; (c) David Shanholtzer Nov 14, 1998 t=0:14:45.24
; P200 MMX 1024x768
; color map: Dav86
reset=1960 type=julia_inverse miim=depth/right
center-mag=0/0/0.6666667 params=-0.013127748/0.701/250 float=y
maxiter=1500 bailout=16 inside=zmag outside=summ
colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\
OSSSWWW___ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zV\
z<3>zVV<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00\
S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2\
>EHSKKS<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3\
>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG\
8AG88G8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2\
>BGFBGGBFGBDGBCG0Pe<6>0J_
}
An_Inverse_Julia2a { ; (c) David Shanholtzer Nov 14, 1998 t=0:14:45.24
; P200 MMX 1024x768
; color map: Dav25c
reset=1960 type=julia_inverse miim=depth/right
center-mag=0/0/0.6666667 params=-0.013127748/0.701/250 float=y
maxiter=1500 bailout=16 inside=zmag outside=summ
colors=000iJnlLq<30>G1IE0GF0G<24>e8bmcw<32>909100<35>J00K00L00M00N00<36>\
w65000<68>D0FE0GG1I<10>gIk
}
An_Inverse_Julia4 { ; (c) David Shanholtzer Nov 15, 1998 t=0:16:11.42
; P200 MMX 1024x768
reset=1960 type=julia_inverse miim=depth/left
center-mag=0/0/0.6666667 params=-0.01325/0.70133/247 float=y
maxiter=35000 inside=zmag
colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\
OSSSWWW___ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zV\
z<3>zVV<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00\
S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2\
>EHSKKS<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3\
>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG\
8AG88G8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2\
>BGFBGGBFGBDGBCGV3V<6>ZAZ
}
An_Inverse_Julia5 { ; (c) David Shanholtzer Nov 15, 1998 t=0:31:35.53
; P200 MMX 1024x768
reset=1960 type=julia_inverse miim=depth/left
center-mag=0/0/0.6666667 params=-0.001975/0.6475/255 float=y
maxiter=750000 inside=zmag
colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\
OSSSWWW___ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zV\
z<3>zVV<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00\
S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2\
>EHSKKS<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3\
>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG\
8AG88G8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2\
>BGFBGGBFGBDGBCGV3V<6>ZAZ
}
And remember, if you walk a mile in someone's shoes, s/he'll be a mile away
and barefoot... :)
davides@pipeline.com
ds30@umail.umd.edu
Back up my hard drive?
How do I put it in reverse?
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------------------------------
Date: Sun, 15 Nov 1998 12:15:15 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: (fractint) Polar Curves coloring
Here are the .frm and .par files for the Polar Curves coloring method that
I mentioned earlier. Both are included in my Fractint stuff collection on
my webpage.
Kerry
- -------------------------------------------------------------------------------
Kerry Mitchell
lkmitch@primenet.com www.primenet.com/~lkmitch/
- -------------------------------------------------------------------------------
*** begin polar.par ***
comment { ; copyright Kerry Mitchell 14nov98
Polar Curves
Typically, points in a plane are thought of in terms of their x- and
y-coordinates, that is, how far away (and on which side) the point is
from the horizontal x-axis and the vertical y-axis. Another way of
looking at the point is with polar coordinates, which specify the
distance of the point from the origin (r) and its direction (t). The
two methods are equivalent:
x = r*cos(t), y=r*sin(t), or
r^2 = x^2 + y^2, tan(t) = y/x.
Polar curves are curves that specify r as a function of t, instead of
y as a function of x. The curve used in this coloring method is:
r = [a * f(b*t)]^n + r0,
where f is one of Fractint's builtin functions (e.g., sin, cos, exp,
etc.), a is an amplitude scaling factor, and b is a frequency factor.
The exponent n is useful for making the curve wider or thinner, and r0
is a expansion or contraction constant.
Some special curves can be generated using this function. Spirals can
be made by using the "ident" function. Here, the exponent n controls
how tightly wound the spiral is. However, only one revolution of the
spiral will be drawn, as t is limited to the range 0 to 2*pi.
"Rose" curves are made by using either sin or cos functions. The
parameter a controls the size of the curve. The number of "petals"
is b, so long as b is a positive integer. Increasing n from 1 will
make the petals thinner; decreasing it toward 0 will make them thicker.
Leave r0=0 for the standard rose curve, where the petals all join at
the origin.
Since the sin and cos functions generate negative values, the "rose"
curves will have some regions of negative r. How this is handled
depends on r0 and "negrflag", the negative r flag. Setting negrflag to
1 will make the routine ignore negative r values. This, with r0 is set
to 0, will cause the rose curve to have "b" number of petals, all of
them the same size. Setting negrflag=2 will make the routine consider
negative r's the same as positive r's. Thus, the rose curve will have
2*b petals. Increasing r0 from 0 will make r positive more often than
negative. This will also increase the number of petals from b to 2*b,
but half of the petals will be small and half will be large.
The best way to see the effects of the parameter choices is to use the
"polar" formula. This formula doesn't draw a fractal, just the polar
curve determined by a, b, n, r0, the chosen function, and the negative r
flag. Another flag determines how the curve is shown. If the coloring
flag "colflag" is set to 1, then the image will be colored by how close
the pixel is to the polar curve. Is essence, this will outline the curve.
If colflag=2, then the area outside of the curve is colored black (color
0), and the inside is rendered in a second color (color 40).
The other formulas use polar curves to color fractals. There are 2
basic rendering methods: how close the orbit comes to the polar curve,
and how often the orbit is inside the polar curve. The "polar-near_man"
and "polar-near_jul" formulas color the Mandelbrot and Julia sets in the
first manner. The "polar-inout_man" and "polar-inout_jul" formulas take
the second tack. In the Julia cases, the bailout value and the negative
r flag are hardcoded, to allow full freedom in specifying a, b, n, and r0.
}
four-leaf-rose { ; set imag(p1)=2 to see effect of negative r
;
; illustrates interior coloring of polar curve
;
reset=1960 type=formula formulafile=test.frm formulaname=polar
function=sin center-mag=0/0/0.7 params=2/1/1/4/1/0 float=y
maxiter=256 inside=0 decomp=256 periodicity=0 cyclerange=0/255
}
near_mandel { ; copyright Kerry Mitchell 14nov98
;
; illustrates "near to polar curve" Mandelbrot coloring
;
reset=1960 type=formula formulafile=polar.frm
formulaname=polar-near_man function=cos center-mag=-0.6/0/0.8
params=1000/1/1/3/3/0 float=y maxiter=28 inside=0 decomp=256
periodicity=0 colors=000<46>00x00z00z<12>08z09z0Az0Bz0Cz<28>\
0mz0oz0oz<12>7xs8yr9zqAzpBzo<44>xz2zz0zz0<46>zR0zR0yQ0yQ0xP0\
<9>rK0qJ0pI0oI0nI0<11>ZC0YC0WB0UB0<13>210 cyclerange=0/255
}
near_julia { ; copyright Kerry Mitchell 14nov98
;
; illustrates "near to polar curve" Julia coloring
;
reset=1960 type=formula formulafile=polar.frm
formulaname=polar-near_jul function=sin center-mag=0/0\
/0.6666667 params=-0.778/0.201/2/2/1/0.4428474 float=y
maxiter=256 inside=0 decomp=256 periodicity=0 colors=000\
<46>00x00z00z<12>08z09z0Az0Bz0Cz<28>0mz0oz0oz<12>7xs8yr9\
zqAzpBzo<44>xz2zz0zz0<46>zR0zR0yQ0yQ0xP0<9>rK0qJ0pI0oI0n\
I0<11>ZC0YC0WB0UB0<13>210 cyclerange=0/255
}
inout_mandel { ; copyright Kerry Mitchell 14nov98
;
; illustrates "inside polar curve" Mandelbrot coloring
;
reset=1960 type=formula formulafile=polar.frm
formulaname=polar-inout_man function=cos center-mag=-0.6/0/0.8
params=1000/2/1/2/1/0 float=y maxiter=256 inside=0 decomp=256
periodicity=0 colors=000<62>00z00z11y<61>zz0zz0zy0<61>z01z01\
z12<61>zzz cyclerange=0/255
}
inout_julia { ; copyright Kerry Mitchell 14nov98
;
; illustrates "inside polar curve" Julia coloring
;
reset=1960 type=formula formulafile=polar.frm
formulaname=polar-inout_jul function=cos center-mag=0/0/0.9/1/10
params=-0.1010946435276083/0.9562770568810802/1/3/1/0 float=y
maxiter=256 inside=0 decomp=256 periodicity=0 colors=000<62>00z\
00z11y<61>zz0zz0zy0<61>z01z01z12<61>zzz cyclerange=0/255
}
*** end polar.par ***
*** begin polar.frm ***
polar { ; Kerry Mitchell 14nov98
;
; draws polar curve r = cabs(a*fn1(b*theta))^n+r0
;
; real(p1) = coloring flag:
; 1 to color by nearness to curve
; 2 to color by inside/outside
; imag(p1) = negative r handling flag:
; 1 to ignore r<0
; 2 to use |r| instead of r
; real(p2) = a = amplitude
; imag(p2) = b = frequency
; real(p3) = n = exponent
; imag(p3) = r0 = baseline
;
; use decomp=256, float=yes, periodicity=no
;
zc=pixel, done=1, twopi=2*pi
a=real(p2), b=imag(p2), n=real(p3), r0=imag(p3)
colflag=real(p1), negrflag=imag(p1)
:
t=imag(log(zc))
if(t<0)
t=t+twopi
endif
r=a*fn1(b*t)
if(r>=0)
r=r^n
else
r=-((-r)^n)
endif
r=r+r0
if(colflag==1)
if(negrflag==1)
err=r-cabs(zc)
else
err=|r|-|zc|
endif
err=cabs(err)
t=log(err)
z=cos(t)+flip(sin(t))
else
if(negrflag==1)
if(r<cabs(zc))
t=0
else
t=1
endif
else
if(|r|<|zc|)
t=0
else
t=1
endif
endif
z=cos(t)+flip(sin(t))
endif
done==0
}
polar-near_man { ; Kerry Mitchell 14nov98
;
; colors Mandelbrot set by orbit's closet approach to
; polar curve r = cabs(a*fn1(b*theta))^n+r0
;
; real(p1) = bailout
; imag(p1) = negative r handling flag:
; 1 to ignore r<0
; 2 to use |r| instead of r
; real(p2) = a = amplitude
; imag(p2) = b = frequency
; real(p3) = n = exponent
; imag(p3) = r0 = baseline
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=0, c=pixel, iter=1, done=0
bailout=real(p1), errmin=bailout
a=real(p2), b=imag(p2), n=real(p3), r0=imag(p3)
twopi=2*pi, negrflag=imag(p1)
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute polar angle t from new value of zc
; adjust t to be in range [0, 2pi]
;
t=imag(log(zc))
if(t<0)
t=t+twopi
endif
;
; find polar radius from angle t
;
r=a*fn1(b*t)
if(r>=0)
r=r^n
else
r=-((-r)^n)
endif
r=r+r0
;
; if negrflag = 1, compare r with magnitude of zc--
; this ignores negative r values
; if negrflag = 2, compare magnitude squared of r
; with magnitude squared of zc--this treats -r as r
;
if(negrflag==1)
err=cabs(r-cabs(zc))
else
err=cabs(|r|-|zc|)
endif
;
; update minimum distance if a new smaller error is found
;
if(err<errmin)
errmin=err
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use log(minimum distance) as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=log(errmin)
z=cos(t)+flip(sin(t))
endif
done==0
}
polar-near_jul { ; Kerry Mitchell 14nov98
;
; colors Julia set by orbit's closet approach to
; polar curve r = cabs(a*fn1(b*theta))^n+r0
;
; p1 = c = Julia parameter
; real(p2) = a = amplitude
; imag(p2) = b = frequency
; real(p3) = n = exponent
; imag(p3) = r0 = baseline
;
; bailout = 1000 (hardcoded)
; negative r handling flag = 1 (hardcoded)
; 1 to ignore r<0
; 2 to use |r| instead of r
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=pixel, c=p1, iter=1, done=0
bailout=1000, errmin=bailout
a=real(p2), b=imag(p2), n=real(p3), r0=imag(p3)
twopi=2*pi, negrflag=1
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute polar angle t from new value of zc
; adjust t to be in range [0, 2pi]
;
t=imag(log(zc))
if(t<0)
t=t+twopi
endif
;
; find polar radius from angle t
;
r=a*fn1(b*t)
if(r>=0)
r=r^n
else
r=-((-r)^n)
endif
r=r+r0
;
; if negrflag = 1, compare r with magnitude of zc--
; this ignores negative r values
; if negrflag = 2, compare magnitude squared of r
; with magnitude squared of zc--this treats -r as r
;
if(negrflag==1)
err=cabs(r-cabs(zc))
else
err=cabs(|r|-|zc|)
endif
;
; update minimum distance if a new smaller error is found
;
if(err<errmin)
errmin=err
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use log(minimum distance) as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=log(errmin)
z=cos(t)+flip(sin(t))
endif
done==0
}
polar-inout_man { ; Kerry Mitchell 14nov98
;
; colors Mandelbrot set by how often orbit is inside
; polar curve r = cabs(a*fn1(b*theta))^n+r0
;
; real(p1) = bailout
; imag(p1) = negative r handling flag:
; 1 to ignore r<0
; 2 to use |r| instead of r
; real(p2) = a = amplitude
; imag(p2) = b = frequency
; real(p3) = n = exponent
; imag(p3) = r0 = baseline
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=0, c=pixel, iter=1, done=0
bailout=real(p1), incount=0
a=real(p2), b=imag(p2), n=real(p3), r0=imag(p3)
twopi=2*pi, negrflag=imag(p1)
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute polar angle t from new value of zc
; adjust t to be in range [0, 2pi]
;
t=imag(log(zc))
if(t<0)
t=t+twopi
endif
;
; find polar radius from angle t
;
r=a*fn1(b*t)
if(r>=0)
r=r^n
else
r=-((-r)^n)
endif
r=r+r0
;
; if negrflag = 1, compare r with magnitude of zc--
; this ignores negative r values
; if negrflag = 2, compare magnitude squared of r
; with magnitude squared of zc--this treats -r as r
;
if(negrflag==1)
err=cabs(zc)-r
else
err=|zc|-|r|
endif
;
; update inside counter if err<0
;
if(err<0)
incount=incount+1
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use ratio of incount to iterations as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=twopi*incount/(iter-1)
z=cos(t)+flip(sin(t))
endif
done==0
}
polar-inout_jul { ; Kerry Mitchell 14nov98
;
; colors Julia set by how often orbit is inside
; polar curve r = cabs(a*fn1(b*theta))^n+r0
;
; p1 = c = Julia parameter
; real(p2) = a = amplitude
; imag(p2) = b = frequency
; real(p3) = n = exponent
; imag(p3) = r0 = baseline
;
; bailout=1000 (hardcoded)
; negative r handling flag = 1 (hardcoded)
; 1 to ignore r<0
; 2 to use |r| instead of r
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=pixel, c=p1, iter=1, done=0
bailout=1000, incount=0
a=real(p2), b=imag(p2), n=real(p3), r0=imag(p3)
twopi=2*pi, negrflag=1
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute polar angle t from new value of zc
; adjust t to be in range [0, 2pi]
;
t=imag(log(zc))
if(t<0)
t=t+twopi
endif
;
; find polar radius from angle t
;
r=a*fn1(b*t)
if(r>=0)
r=r^n
else
r=-((-r)^n)
endif
r=r+r0
;
; if negrflag = 1, compare r with magnitude of zc--
; this ignores negative r values
; if negrflag = 2, compare magnitude squared of r
; with magnitude squared of zc--this treats -r as r
;
if(negrflag==1)
err=cabs(zc)-r
else
err=|zc|-|r|
endif
;
; update inside counter if err<0
;
if(err<0)
incount=incount+1
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use ratio of incount to iterations as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=twopi*incount/(iter-1)
z=cos(t)+flip(sin(t))
endif
done==0
}
*** end polar.frm ***
- --------------------------------------------------------------
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Date: Sun, 15 Nov 1998 12:17:30 -0700 (MST)
From: Kerry Mitchell <lkmitch@primenet.com>
Subject: (fractint) Astroid coloring method
Here are the .frm and .par files for the Astroid coloring method that I
mentioned earlier. Both are included in my Fractint stuff collection on
my webpage.
Kerry
- -------------------------------------------------------------------------------
Kerry Mitchell
lkmitch@primenet.com www.primenet.com/~lkmitch/
- -------------------------------------------------------------------------------
*** begin astroid.par ***
comment { ; copyright Kerry Mitchell 14nov98
Astroid
The astroid is a figure from analytic geometry, resembling a four-
pointed star with concave sides. Its defining equation is:
x^(2/3) + y^(2/3) = a^(2/3)
where a determines the size of the figure, similar to the radius of
a circle. This equation can be generalized by changing the exponent
of 2/3 to any value n. If n is between 0 and 1, the figure resembles
the standard astroid. The sides go from being straight lines for n=1
to lying atop of the coordinates axes as n approaches 0. For n>1, the
figure becomes convex, and is a circle for n=2. As n approaches
infinity, the figure approaches a square.
This generalized astroid is the basis of this coloring scheme. As with
other plane figures, the astroid can be compared to the Mandelbrot and
Julia orbits. In the "astroid-near_man" and "astroid-near_jul" formulas,
the fractal is colored according to the closest approach of the orbit
to the figure. The "astroid-inout_man" and "astroid-inout_jul" figures
color by how often the orbit lands inside the astroid.
The shape of the astroid can be altered through the exponent n, and its
size changed through the use of a. In addition, its orientation and
location in the plane are determined by a "center" and "rotation"
parameters. The effects of all these parameters can be investigated
using the basic "astroid" formula. Here, the coloring flag allows 2
ways of viewing the astroid: in outline (colflag=1) and by coloring
the inside vs. the outside (colflag=2).
}
basic-astroid { ; set real(p1)=2 to see inside
;
; illustrates astroid drawing
;
reset=1960 type=formula formulafile=astroid.frm formulaname=astroid
center-mag=0/0/0.6666667 params=1/0/1/0.666666666/0/0 float=y
maxiter=256 inside=0 decomp=256 periodicity=0 cyclerange=0/255
}
square-mandel { ; copyright Kerry Mitchell 14nov98
;
; illustrates "near astroid" Mandelbrot coloring
;
reset=1960 type=formula formulafile=astroid.frm
formulaname=astroid-near_man center-mag=-0.25/0/0.7
params=1000/0/0.01/20/0/0 float=y maxiter=100 inside=0
decomp=256 periodicity=0 colors=zzzuzzryz<5>jvzivziuz<7>\
bqybqyapyapy`ox<8>WkwVjvVjvViv<7>RetQesQdsQdrPcr<25>GSfF\
RfFReFQd<13>AJXAJWAIV9IU9HU<33>001000001<31>8GS9HT9HU9IU\
AIVAJW<31>KYmLZnLZnM_oM_o<11>RetRftSftSgtTgu<4>VjvVjvWkw\
Xkw<11>bqycrydryesyesz<5>jvzkwzmwz<2>qyzryzuzz cyclerange=0/255
}
sprites { ; copyright Kerry Mitchell 14nov98
;
; illustrates "near astroid" Julia coloring
;
reset=1960 type=formula formulafile=astroid.frm
formulaname=astroid-near_jul center-mag=0/0/0.6666667
params=0/1/0.6666666666666666/0.3333333333333333/-2/0
float=y maxiter=7 inside=0 decomp=256 periodicity=0
colors=FF`<3>DDXDDWDDVDDUCCT<28>000000110<60>yn0zo0zo\
0zo1<61>zzzzzzyyz<60>QQzPPzPPzPPy<23>FFa cyclerange=0/255
}
astroid-near-julia { ; copyright Kerry Mitchell 14nov98
;
; illustrates "inside astroid" Mandelbrot coloring
;
reset=1960 type=formula formulafile=astroid.frm cyclerange=0/255
formulaname=astroid-inout_man decomp=256 periodicity=0
center-mag=-1.27693934506353900/+0.35261951597131690/274914.1
params=1000/0/0.75/0.5/-0.75/0 float=y maxiter=256 inside=0
colors=000<62>00z00z11y<61>zz0zz0zy0<61>z01z01z12<61>zzz
}
neptune { ; copyright Kerry Mitchell 14nov98
;
; illustrates "inside astroid" Julia coloring
;
reset=1960 type=formula formulafile=astroid.frm
formulaname=astroid-inout_jul center-mag=0/0/0.6666667
params=-0.735038819963/0.14041387858/2/0.5/1/0 float=y
maxiter=256 inside=0 decomp=256 periodicity=0 colors=000\
<30>xm0zo0zo1<29>zyxzzzyyz<29>RRzPPzPPy<30>000<30>yn0zo0\
zo2<29>zyyzzzyyz<29>QQzPPzOOx<29>111 cyclerange=0/255
}
*** end astroid.par ***
*** begin astroid.frm ***
astroid { ; Kerry Mitchell 14nov98
;
; draws a astroid: x^n + y^n = a^n
;
; real(p1) = coloring flag:
; 1 to color by nearness to curve
; 2 to color by inside/outside
; imag(p1) = rotation angle
; real(p2) = a = size
; imag(p2) = n = exponent
; p3 = astroid center
;
; use decomp=256, float=yes, periodicity=no
;
zc=pixel, done=1, colflag=real(p1)
a=real(p2), n=imag(p2), aton=a^n
center=p3, rot=imag(p1)/180*pi, rot=exp(flip(rot))
:
temp=rot*(zc-center)
x=cabs(real(temp)), y=cabs(imag(temp))
err=x^n+y^n-aton
if(colflag==1)
t=log(cabs(err))
else
if(err<0)
t=1
else
t=0
endif
endif
z=cos(t)+flip(sin(t))
done==0
}
astroid-near_man { ; Kerry Mitchell 14nov98
;
; colors Mandelbrot set by orbit's closet approach to
; a astroid: x^n + y^n = a^n
;
; real(p1) = bailout
; imag(p1) = rotation angle, degrees
; real(p2) = a = size
; imag(p2) = n = exponent
; p3 = center of astroid
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=0, c=pixel, iter=1, done=0
bailout=real(p1), errmin=bailout
a=real(p2), n=imag(p2), aton=a^n
center=p3, rot=imag(p1)/180*pi, rot=exp(flip(rot))
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute difference between actual location and
; astroid location; update minimum if necessary
;
temp=(zc-center)*rot
x=cabs(real(temp)), y=cabs(imag(temp))
err=cabs(x^n+y^n-aton)
if(err<errmin)
errmin=err
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use log(minimum) as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=log(errmin)
z=cos(t)+flip(sin(t))
endif
done==0
}
astroid-near_jul { ; Kerry Mitchell 14nov98
;
; colors Julia set by orbit's closet approach to
; a astroid: x^n + y^n = a^n
;
; p1 = c = Julia parameter
; real(p2) = a = size
; imag(p2) = n = exponent
; p3 = center of astroid
; bailout = 1000 (hardcoded)
; rotation angle, degrees = 0 (hardcoded)
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=pixel, c=p1, iter=1, done=0
bailout=1000, errmin=bailout
a=real(p2), n=imag(p2), aton=a^n
center=p3, rot=0/180*pi, rot=exp(flip(rot))
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute difference between actual location and
; astroid location; update minimum if necessary
;
temp=(zc-center)*rot
x=cabs(real(temp)), y=cabs(imag(temp))
err=cabs(x^n+y^n-aton)
if(err<errmin)
errmin=err
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use log(minimum) as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=log(errmin)
z=cos(t)+flip(sin(t))
endif
done==0
}
astroid-inout_man { ; Kerry Mitchell 14nov98
;
; colors Mandelbrot set by how often orbit is inside
; a astroid: x^n + y^n = a^n
;
; real(p1) = bailout
; imag(p1) = rotation angle, degrees
; real(p2) = a = size
; imag(p2) = n = exponent
; p3 = center of astroid
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=0, c=pixel, iter=1, done=0
bailout=real(p1), incount=0, speed=2*pi
a=real(p2), n=imag(p2), aton=a^n
center=p3, rot=imag(p1)/180*pi, rot=exp(flip(rot))
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute difference between actual location and
; astroid location; update minimum if necessary
;
temp=(zc-center)*rot
x=cabs(real(temp)), y=cabs(imag(temp))
err=x^n+y^n-aton
if(err<0)
incount=incount+1
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use incount/iterations as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=speed*incount/(iter-1)
z=cos(t)+flip(sin(t))
endif
done==0
}
astroid-inout_jul { ; Kerry Mitchell 14nov98
;
; colors Julia set by how often orbit is inside
; a astroid: x^n + y^n = a^n
;
; p1 = c = Julia parameter
; real(p2) = a = size
; imag(p2) = n = exponent
; p3 = center of astroid
; bailout = 1000 (hardcoded)
; rotation angle, degrees = 0 (hardcoded)
;
; colors inside & outside points the same way
; use decomp=256, float=yes, periodicity=no
;
zc=pixel, c=p1, iter=1, done=0
bailout=1000, incount=0, speed=2*pi
a=real(p2), n=imag(p2), aton=a^n
center=p3, rot=0/180*pi, rot=exp(flip(rot))
:
;
; standard iteration
;
iter=iter+1, zc=sqr(zc)+c
;
; compute difference between actual location and
; astroid location; update minimum if necessary
;
temp=(zc-center)*rot
x=cabs(real(temp)), y=cabs(imag(temp))
err=x^n+y^n-aton
if(err<0)
incount=incount+1
endif
;
; bailout at escape or maximum iterations
; set "done" flag
; use incount/iterations as angle for decomp coloring
;
if((|zc|>bailout)||(iter==maxit))
done=1
t=speed*incount/(iter-1)
z=cos(t)+flip(sin(t))
endif
done==0
}
*** end astroid.frm ***
- --------------------------------------------------------------
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------------------------------
Date: Sun, 15 Nov 1998 14:24:17 -0500
From: JoWeber <JoWeber@compuserve.com>
Subject: (fractint) motw007
Hi All,
I added the Mandel of the Week 7 and some new sites.
Enjoy --Jo--
http://ourworld.compuserve.com/homepages/joweber
- --------------------------------------------------------------
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Date: Sun, 15 Nov 1998 13:24:45 -0800
From: "Jay Hill" <ehill1@san.rr.com>
Subject: Re: (fractint) motw007
Hi Jo,
OK, so it took 159 hours to generate the image, but how many to find it?
From your page...
http://ourworld.compuserve.com/homepages/joweber/jo_03.htm
what does this mean:
The Image is created at 1600x1200 and then saved with fractint at 800x600.
Don't you have to recalc at 800x600?
The last line of the par misses a C/R (I fixed this in my copy)
2>zK0zH0zE0zB0z70z40z00<10>Z00W00T00Q00N00<8>100<12>h2gk2jm2no2qr3utIv<4\
>zzz<10>Zjz
finally why do I get this message when I try to load the par into Fractint...
- ------
Oops. I couldn't understand the argument:
center-mag=-1.94052699850330403982402612983984930363482192014828248165
Any key to continue...
- ------
I even made the lines half as long with the usual \ to cut them.
Anyone know?
OK, I'm confused!! Next I copied the gif image to disk and loaded it for
viewing
without difficulty. Then used 'B' command to save it to a par. Now I compare
this par with that copied directly from the web page. I can't see a difference
but Fractint gets above error message on the par snipped from the web
page but no error from the par generated locally from the gif.
Now what gives? Many of my images are posted as .jpg or as 1/2 resolution gif
for compression. I also display the par. Now it looks like this is bound to
give some folk trouble. Great...
Wait, here is a test .par anyone should be able to duplicate the problem
with...
http://home.san.rr.com/jayrhill/12.par (save to your disk to try)
Now image par '1' loads ok, image par '2' does not and they are binary (hex)
identicals
as far as I can see!!!!!
Jay
- ----------
From: JoWeber <JoWeber@compuserve.com>
To: INTERNET:fractint@lists. <fractint@lists.xmission.com>
Subject: (fractint) motw007
Date: Sunday, November 15, 1998 11:24 AM
Hi All,
I added the Mandel of the Week 7 and some new sites.
Enjoy --Jo--
http://ourworld.compuserve.com/homepages/joweber
- --------------------------------------------------------------
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Date: Sun, 15 Nov 1998 16:48:49 -0500
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: Re: (fractint) motw007
Hi Jay,
>> Wait, here is a test .par anyone should be able to duplicate the probl=
em
>> with... http://home.san.rr.com/jayrhill/12.par (save to you=
r
>> disk to try) Now image par '1' loads ok, image par '2' does not and th=
ey
>> are binary (hex) identicals as far as I can see!!!!!
No, they are not identical! There's an extra space after the "\" in th=
e
second line of the center-mag section, just delete it and "2" will load o=
k.
Cheers,
- Sylvie
- --------------------------------------------------------------
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Date: Sun, 15 Nov 1998 14:06:45 -0800
From: "Jay Hill" <ehill1@san.rr.com>
Subject: Re: (fractint) motw007
Thank you for the quick reply. The HEX is more precise than ASCII. I was
using PC MAGAZINE's compare.com which showed marks on spaces but
not at hte end of the lines.
Now I wanted to see what the early zooms look like. We can't edit the zoom in
fractint
so I edited the working par file like this
MotW007-x-goof_up { ; at 1280x1024 (Jay Hill experimenting with...
; http://ourworld.compuserve.com/homepages/joweber/jo_03.h
; on a P133 at 1600x1200 Nov 14, 1998 21:32:30
; Par and Image Copyright 1998 by Jo Weber
reset=1960 type=mandel
center-mag=-1.94052699850330400/+0.00000001506577993/1.770042e+015/1.178\
2/-80/0.738 params=0/0 float=y maxiter=6666 inside=0
colors=000Xhz<5>I`yG_yEYyCXy9Wy<3>0Qx1Ru2Tq<7>JfWLhTPjV<2>_obbpdeqfirhls\
k<3>zyt<6>zb0<5>zq1zt2zw2zz3vz6<8>Kw_<5>Ets<6>000B15<4>w0P<2>l5Kh7Id8G`9\
EXBC<5>993<2>FG6HI7IK7JN8<2>NVAPYBOVB<3>KJ9JF8JE7<2>IB6<6>qW0sb0<5>zz9<7\
>OnRJlUEkWAiZ5h`0fb<2>7ai<5>YFw<6>D78B30<6>f50<9>xt4zz0<12>zK0zH0zE0zB0z\
70z40z00<9>a00Z00W00T00Q00<9>100<12>h2gk2jm2no2qr3utIv<4>zzz<10>Zjz
}
then after a few zooms I get this bands of garbage showing me we were not
getting into deep zoom mode. Several more zooms resulted in this...I never got
into
extended precision mode!!! Using 320x200 does not help.
{{{
cvtcentermag problem
xxmin= -1.#IND0000000000000000 xxmax= -1.#IND0000000000000000
yymin= -1.#IND0000000000000000 yymax= -1.#IND0000000000000000
xx3rd= -1.#IND0000000000000000 yy3rd= -1.#IND0000000000000000
delxx= 0.00000000000000000000 delyy= 0.00000000000000000019
delx2= 0.00000000000000000223 dely2= -0.00000000000000000070
Any key to continue...
}}}
I'm now proceeding through this mess by editing the par file. There is
something
screwy going on. I've never seen this before, and I've deep zoomed a few...
Jay
- ----------
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
To: Blind.Copy.Receiver@compuserve.com
Subject: Re: (fractint) motw007
Date: Sunday, November 15, 1998 1:48 PM
Hi Jay,
>> Wait, here is a test .par anyone should be able to duplicate the problem
>> with... http://home.san.rr.com/jayrhill/12.par (save to your
>> disk to try) Now image par '1' loads ok, image par '2' does not and they
>> are binary (hex) identicals as far as I can see!!!!!
No, they are not identical! There's an extra space after the "\" in the
second line of the center-mag section, just delete it and "2" will load ok.
Cheers,
- Sylvie
- --------------------------------------------------------------
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End of fractint-digest V1 #332
******************************