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1998-04-26
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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #176
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Sunday, April 26 1998 Volume 01 : Number 176
----------------------------------------------------------------------
Date: Sun, 26 Apr 1998 16:01:58 -0400
From: Paul Derbyshire <pderbysh@usa.net>
Subject: Re: (fractint) Strngy Mandlebrot
Gedeon Peteri wrote:
> I have no idea why this is so, since the seahorse valley of the full m-set does not
> have those strings extending into the middle of the valley. One of the
> mathematicians on this list will have to enlighten us about that.
All minibrots have strings or some kind of dendrites attached. If you find, on
the set, a minibrot in the middle of a dendrite, then the part of the dendrite
attached to the nose of the minibrot is repeated attached to all of the
minibrot's external angles of the form m/2^n. IOW, the tops of seahorses, the
tails ofelephants, the tips of some dendrites and forks, the ends of spikes...
These are strings if the minibrot came from the spike...
- --
.*. "Clouds are not spheres, mountains are not cones, coastlines are not
- -() < circles, and bark is not smooth, nor does lightning travel in a
`*' straight line." ------------------------------------------------
-- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca
______________________ ____|_____________ pderbysh@usa.net
Programmer & Humanist | ICQ: 10423848 | http://chat.carleton.ca/~pderbysh
- -
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------------------------------
Date: Sun, 26 Apr 1998 16:02:52 -0400
From: Paul Derbyshire <pderbysh@usa.net>
Subject: Re: (fractint) Fractal Chatting
Felix wrote:
>
> This note on chating makes me think: How many of you are on ICQ?
I am...
- --
.*. "Clouds are not spheres, mountains are not cones, coastlines are not
- -() < circles, and bark is not smooth, nor does lightning travel in a
`*' straight line." ------------------------------------------------
-- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca
______________________ ____|_____________ pderbysh@usa.net
Programmer & Humanist | ICQ: 10423848 | http://chat.carleton.ca/~pderbysh
- -
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------------------------------
Date: Sun, 26 Apr 1998 15:08:31 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: (fractint) formula tips
Some time ago I posted a message to the list where I said:
>The reason I've been posting formulas and pars to this list
>is not to show off images, but in the hope that people would
>use the methods to create their own images and perhaps extend
>the methods to other equations or to modify the methods to
>generate new effects.
and:
>Sometime in the near future I'll try to post some tips that will
>make it easier to use the formulas I have posted and will post.
Although I do experiment with new equations from time to time, much
of the fun of fractals for me is inventing new ways to render
existing equations such as the classic Mandelbrot set equation. I've
provided pars with the formulas mainly as a demonstration of what can
be done with the rendering method and, in all cases, they represent
only a tiny sampling of the zillions of nice images that the formula
can produce. It is somewhat more difficult finding all those nice
images using my rendering methods than it is using the tradional
methods, so the purpose of this message is to give those tips I'd
promised for help in using my formulas.
I'll use the classic Mandelbrot set as an example. The formulas
I've posted so far that iterate the Mandelbrot set equation
(z=z*z+c) include:
3D_Balls_Mset
Astroid_Mset
Bubbles_Julia_Mset
Cdp_Jul_Mand
FlexBalls_Mand
Mand_Atan_Mset
Mandel_3Way
Mandel_Squares
with several more to come.
There are three methods you can use to locate nice images:
1. Start plotting one of pars I provided. Then press the 'z'
key, then the 'F6' key, then the 'F4' key, then 'Enter' twice.
This will plot the whole Mandelbrot set (and in most cases will
plot the whole, or nearly the whole, Mset for whatever equation
is iterated). Chances are, the stalks, balls or whatever the
3D-like elements are, will obliterate much of the detail at the
edges of the set. Try reducing the parameter, usually real(p1),
that controls the size of the elements until you have some detail
at the edges of the set. Then zoom into the areas of detail.
If the elements are too small you can now try increasing the
parameter that controls their size.
2. In some of my formulas I've provided a parameter that sets the
value for a variable that I've called "iters_to_skip" or just "skip."
For these formulas, plot the whole Mandelbrot set as described
above, and then try increasing this parameter to 5, 10, 20, 50 or
whatever it takes to uncover the area of interest. The reason this
works is because every pixel within an element has the same iteration
count, and the larger the element, the fewer iterations it represents.
Once you uncover an area and zoom into it, you cannot reduce the
number of iterations to skip without covering the area up again.
3. Find interesting areas using the builtin Mandel type. You can
do this quickly without regard to colors and using float=no. With
the image dispayed, press the 'b' and save the par file. Then,
using a text editor that provides multiple windows (I use the editor
that came with Turbo C++) or multiple instances of Notepad, make a
copy of one of the par files I provided, rename it, and replace the
"center-mag=" or "corners=" info with that from the par file you
created. Run the modified par file and change the size parameter
and colors to get the image you want.
That's about all I can think of for now. Let me know if you find
this useful or if you have any other suggestions.
Paul Carlson
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------------------------------
Date: Sun, 26 Apr 1998 15:14:14 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: (fractint) Newton grapevines formula
comment {
This formula is a Newton's method solution of
w^4 + a*w^3 - 4*w^2 - a*w + 3 = 0, where 'a' is a function
of pixel (I don't remember how I arrived at the function).
Some notes on the pars:
Grapevines: Imagine youself lying on the ground under some
grapevines on a planet in a far galaxy, looking
off towards the horizon.
Newt_elephant: This is not a zoom into elephant valley on one
the midgets, yet the similarities between this
image and the elephants of z=z*z+c are striking.
The midgets: A sampling of the midgets produced by this formula.
All use the same colors - better colors needed!
Enjoy!
Paul Carlson
}
frm:Newt5_Stalks_Mset {; Copyright (c) Paul W. Carlson, 1998
;
; real(p1) = a factor controlling the size of the stalks
; imag(p1) = minimum iterations
; real(p2) = number of color ranges
; imag(p2) = number of colors in a range
; real(p3) = value of |w| for bailout
;
rc = real(pixel), c = pixel - 2 * rc * (rc > 0)
a = 3 * c - 1 / c
w = (sqrt(9 * a * a + 96) - 3 * a) / 12
z = bailout = iter = range_num = 0
stalk_width = real(p1)
num_ranges = real(p2)
colors_in_range = imag(p2)
index_factor = (colors_in_range - 1) / stalk_width
prev_mod2 = |w|
:
w2 = w * w
w = (3*w2*w2 + 2*a*w*w2 - 4*w2 - 3)/(4*w*w2 + 3*a*w2 - 8*w - a)
;
IF (abs(real(w)) <= abs(imag(w)))
dist = abs(real(w))
ELSE
dist = abs(imag(w))
ENDIF
IF (dist < stalk_width && iter > imag(p1))
z = index_factor * dist + range_num * colors_in_range + 1
bailout = 1
ELSEIF (abs(|w| - prev_mod2) < 0.000001)
bailout = 1
z = 252
ENDIF
prev_mod2 = |w|
range_num = range_num + 1
IF (range_num == num_ranges)
range_num = 0
ENDIF
iter = iter + 1
z = z - iter
bailout == 0 && |w| < real(p3)
}
grapevines { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.txt
formulaname=newt5_stalks_mset passes=1
corners=0.869433581427139/0.869433512026894/1.31486394703682/\
1.31486427722428/0.869433397953073/1.31486419166891
params=0.2/0/2/125/1e+020/0
float=y maxiter=256 inside=253 outside=summ
colors=000mZy<96>I0JI0JI0JI0JI0J<22>I0Jiya<123>3D000000z000000000
}
midget5_1 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.frm
formulaname=newt5_stalks_mset passes=t
center-mag=+0.64242363770506840/-0.75947812772406030/5.794176\
e+008/1/-12.499
params=0.2/0/2/125/1e+020/0
float=y maxiter=2000 inside=253 outside=summ
colors=000z88<123>O00zqa<123>WRF000KKm000000kkk
}
midget5_2 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.frm
formulaname=newt5_stalks_mset passes=t
corners=0.869473917831/0.8693836975/1.3146365079/1.3150657515\
/0.869235401546/1.3149545296
params=0.2/0/2/125/1e+020/0
float=y maxiter=1000 inside=253 outside=summ
colors=000z88<123>O00zqa<123>WRF000KKm000000kkk
}
midget5_3 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.frm
formulaname=newt5_stalks_mset passes=t
center-mag=+0.64143261032474960/-0.76003209999604020/102644.1\
/1/-95.5
params=0.15/0/2/125/1e+020/0
float=y maxiter=2000 inside=253 outside=summ
colors=000zqa<123>WRFz88<123>O00000KKm000000000
}
midget5_4 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.frm
formulaname=newt5_stalks_mset passes=t
center-mag=+0.33424946523291680/-0.39784353749430370/327656.2\
/1/3.5
params=0.2/0/2/125/1e+020/0
float=y maxiter=1000 inside=253 outside=summ
colors=000z88<123>O00zqa<123>WRF000KKm000000kkk
}
midget5_5 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.frm
formulaname=newt5_stalks_mset passes=t
center-mag=+5.03160103044942500/+6.52565802349076100/1.295945\
e+007/1/-128.999
params=0.034/0/2/125/1e+020/0
float=y maxiter=1000 inside=253 outside=summ
colors=000zqa<123>WRFz88<123>O00000KKm000000000
}
newt_elephant { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=newt5m.frm
formulaname=newt5_stalks_mset passes=t
corners=0.64194046213/0.64242274401/-0.7614339006/-0.75886431\
58/0.64088068267/-0.7600208616
params=0.2/0/2/125/1e+020/0
float=y maxiter=2000 inside=253 outside=summ
colors=000z88<123>O00zqa<123>WRF000KKm000000kkk
}
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------------------------------
Date: Sun, 26 Apr 1998 16:13:07 -0400
From: Paul Derbyshire <pderbysh@usa.net>
Subject: (fractint) Posting PARs and FRms
I think it is best now if the PARs and FRMs are actually posted both in the
message body and as an attachment. The reason? Although text-based email renders
the former easierto use, Netscape mail and others make the latter easier to use.
(If I copy andpaste a formula from the body of an email in a Windows mail client
it ends up running all on one line for some reason!)
- --
.*. "Clouds are not spheres, mountains are not cones, coastlines are not
- -() < circles, and bark is not smooth, nor does lightning travel in a
`*' straight line." ------------------------------------------------
-- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca
______________________ ____|_____________ pderbysh@usa.net
Programmer & Humanist | ICQ: 10423848 | http://chat.carleton.ca/~pderbysh
- -
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------------------------------
Date: Sun, 26 Apr 1998 16:34:16 -0400
From: Paul Derbyshire <pderbysh@usa.net>
Subject: (fractint) I'm deprived! No fractals of the night anymore! I need my FIX!
Why oh why has the FOTN site been removed, without any advance warning at all?
:-(
All I get when I choose my bookmark to the FOTN index, is Netscape spins its
wheels for hours before announcing that it no longer exists. :-(
- --
.*. "Clouds are not spheres, mountains are not cones, coastlines are not
- -() < circles, and bark is not smooth, nor does lightning travel in a
`*' straight line." ------------------------------------------------
-- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca
______________________ ____|_____________ pderbysh@usa.net
Programmer & Humanist | ICQ: 10423848 | http://chat.carleton.ca/~pderbysh
- -
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------------------------------
Date: Sun, 26 Apr 1998 16:32:56 -0500
From: "Jon Camp" <jon.camp@valpo.edu>
Subject: (fractint) self-similarity
OK, I've seen a lot self-similar areas before but this one continues to
befuddle me. All self-similar areas I have seen before, well, look
self-similar. For example a spiral. But this one doesn't look like any
spiral I've seen before. I zoomed in to about 1+e20 and have yet to see a
minibrot at the center. If anybody else has seen something like please
enlighten me.
full image: http://152.228.63.174/ftp_cnspace/fract186.gif
jcamp1 { ; jon camp
; http://www.valpo.edu/home/student/jcamp/index.html
reset=1960 type=mandel
center-mag=+0.28348295716327030/+0.01034503912890549/1.719957e+010
params=0/0 float=y maxiter=1024
colors=C0C5PP<60>czzczzbyy<52>1LLUF0<54>zzrzzrzyq<66>WI3VH2VG1UF00KK<2>1\
LL1LL2MM2NN<2>4OO
}
jon camp
valparaiso university
//***chaotic n-space network***\\\
http://www.valpo.edu/home/student/jcamp
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------------------------------
Date: Sun, 26 Apr 1998 15:23:33 -0700
From: "Angela Wilczynski" <wizzle@beachnet.com>
Subject: Re: (fractint) I'm deprived! No fractals of the night anymore! I need my FIX!
Paul....
I had no trouble finding Dr. J and FOTN at
http://home.san.rr.com/jayrhill/FotN/FotNindx.html
Maybe you were spinning the wrong wheels???
Angela
Paul Derbyshire wrote:
>
> Why oh why has the FOTN site been removed, without any advance warning at all?
> :-(
>
> All I get when I choose my bookmark to the FOTN index, is Netscape spins its
> wheels for hours before announcing that it no longer exists. :-(
>
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------------------------------
Date: Sun, 26 Apr 1998 18:14:02 -0400
From: Gedeon Peteri <gedeon@InfoAve.Net>
Subject: (fractint) pars of Paul Carlson frms
Paul,
Your incredible output of great formulas continues at a pace I cannot
keep up with, but by all means keep them coming! As the pars below show,
I am far behind. I haven't even gotten to any of the midgets yet! The
pars you posted these past few days are sublime!
Gedeon
caperpil { ; (c) Gedeon Peteri, Apr 26, 1998
; Formula by Paul Carlson
reset=1960 type=formula formulafile=pcarlson.frm
formulaname=ibubs_julia_mset passes=1
center-mag=9.18614/5.862/0.2209658
params=0.2956/0.4830000000000001/0.41/16/2/125
float=y maxiter=10000 outside=summ
colors=000hTEeSEdQD<6>PFD2FC<8>BTDCVDDWEEXE<4>\
HbEIcEIcEJdE<3>KeFKfFKeFJeFJeF<4>HbEHaEG`EF_E<6>\
9QD8PD7ND6LC<3>2FC999<4>GGGHHHIIIJJJLLL<7>TTTTTTUU\
UUUUVVV<2>VVVWWWVVV<2>VVVUUUUUUTTTTTT<11>GGGEEEDDD\
BBBAAA999UPF<4>cXMdZNg_O<5>phVriWsjXtkY<3>xn_xo`yo`\
yo`yo`zpa<2>yo`xo`xn_wm_<4>riWphVofU<3>haPg_OdZN<5>\
UPFH00<2>N00O00R00<3>Y00Z00`00a00c00<6>j00j00k00k00\
k00l00<3>j00j00i00h00<4>c00a00`00Z00Y00<2>S00R00O00\
<2>J00H00H00RHD<4>aPDdQDeSEhTEiVElWE<4>saEubEucEwc\
EwdFxeF<2>yeFzfFyeFyeFyeFxeFwdFwcEucEubE<4>mXElWEiVE
}
gp-cmj01 { ; (c) Gedeon Peteri, Apr 25, 1998
; Formula by Paul Carlson
reset=1960 type=formula formulafile=pcarlson.frm
formulaname=cdp_jul_mand passes=1
center-mag=0.21551/-0.482882/12.72076
params=1/0.275/0.39937/-0.272/2/120 float=y
maxiter=5000 inside=0 outside=summ logmap=4
colors=000T0F<10>K0DDEI<37>fglghmfgl<38>DEIC85<36>\
mfangbnfa<38>C85000<15>000100301<28>t0Kv0Lv0L<33>U0F
}
gp-cmj02 { ; (c) Gedeon Peteri, Apr 25, 1998
; Formula by Paul Carlson
reset=1960 type=formula formulafile=pcarlson.frm
formulaname=cdp_jul_mand passes=1
center-mag=0.271052/-0.436024/11.64404
params=1/0.275/-0.18/0.67/2/120 float=y
maxiter=5000 inside=0 outside=summ logmap=4
colors=CIQBFN<37>iipiiphho<37>GFNOD0<6>UJ0VJ1WK1XL\
2YM2<27>vhHwiHwiIwjI<3>wnKwnLwoLwoLwnK<4>wjIwiHvh\
HugG<28>VK1UJ0UI0TH0<4>OD0HBF<37>jdikejjdi<38>HBF
}
gp-ibubj-01 { ; (c) Gedeon Peteri, Apr 26, 1998
; Color map by Paul Carlson
; Formula by Paul Carlson
reset=1960 type=formula formulafile=pcarlson.frm
formulaname=ibubs_julia_mset passes=1
center-mag=1.58508/0.796984/5.004955/1/-17.5
params=0.31133/-0.0074/0.41/16/2/125 float=y
maxiter=10000 outside=summ
colors=000zz0<123>aG0zVz<123>L5L000<3>000
}
gp-ibubj-02 { ; (c) Gedeon Peteri, Apr 26, 1998
; Formula by Paul Carlson
reset=1960 type=formula formulafile=pcarlson.frm
formulaname=ibubs_julia_mset passes=1
center-mag=-1.03898/3.53314/4.149141
params=-0.17333/0.6515/0.21/16/2/125 float=y
maxiter=10000 outside=summ
colors=000UUU<2>TTTSSSRRRQQQPPP<7>GGGEEEDDDBBBAAA\
999UPF<4>cXMdZNg_O<5>phVriWsjXtkY<3>xn_xo`yo`yo`yo`\
zpa<2>yo`xo`xn_wm_<4>riWphVofU<3>haPg_OdZN<5\
>UPFH00<2>N00O00R00<3>Y00Z00`00a00c00<6>j00j00k00k\
00k00l00<3>j00j00i00h00<4>c00a00`00Z00Y00<2>S00R0\
0O00<2>J00H00H00RHD<4>aPDdQDeSEhTEiVElWE<4>sa\
EubEucEwcEwdFxeF<2>yeFzfFyeFyeFyeFxeFwdFwcEucEubE\
<4>mXElWEiVEhTEeSEdQD<6>PFD2FC<8>BTDCVDDWEEXE<4>\
HbEIcEIcEJdE<3>KeFKfFKeFJeFJeF<4>HbEHaEG`EF_E<6\
>9QD8PD7ND6LC<3>2FC999<4>GGGHHHIIIJJJLLL<7>TTTTTT\
UUUUUUVVV<2>VVVWWWVVV<2>VVV
}
gp-mej-02 { ; (c) Gedeon Peteri, Apr 25, 1998
; Formula by Paul Carlson
reset=1960 type=formula formulafile=pcarlson.frm
formulaname=myeqn_julia passes=1
center-mag=2.40072/-0.587147/7.038499
params=0.5175/-0.5847/4/0.07000000000000001/2/125
float=y maxiter=1000 inside=253 outside=summ
colors=CIGXc`<27>CIG0M5<46>0uD0vD0uD<45>0M5DEI\
<37>fglghmfgl<38>DEIDJH<36>dkhelidki<9>Yda
}
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------------------------------
Date: Sun, 26 Apr 1998 18:14:19 -0400
From: Lee Skinner <LeeHSkinner@compuserve.com>
Subject: (fractint) sprouts
Here's another hypercomplex image that I thought was pretty:
hycp067 { ; sprouts t=3D 0:17:07.75
; on a P233 at 1600x1200 Apr 26, 1998 16:08:57
; Image Copyright 1998 by Lee H. Skinner ver=3D1961
reset=3D1961 type=3Dhypercomplex function=3Dsqr passes=3D1
center-mag=3D-0.74920905770129600/+0.00066346753550516/29495.0\
7/1/-90 params=3D0/0/0.1/0 float=3Dy maxiter=3D1023 inside=3D0
logmap=3Dyes symmetry=3Dnone periodicity=3D0
colors=3D000FB3zzz<9>__XXXUVURSROPOL<3>EDBBB9887665333000<6>2L\
G3OI3RL<3>5bUv0_<3>xOixUky_nyepzls<3>zvszytuxt<3>`tvWrwRqw<3\
>6my<3>4Sy3Ny3Hy<2>00z<3>NNyTTxZZx<2>3pw<3>nxyzzzzvw<3>ychyZ\
dyV`yQX<2>wCM<3>bADYABS99N97H84<18>MB5MB5NB5NB5NB5OC6NB5<4>L\
O3LR3KU2<2>Ja1Id0Id0<12>DS2CR2CQ2<2>BN2AM38K45I5<2>0C0<3>AB0\
CA1BA1<3>681581371271062<3>mA4zC5zK7<3>zpG<4>zzdzuMyp3<3>yW3\
yQ4yO5<3>yG5zE6vH8<11>K56H45D35A25715304202000000<7>O09R0AU0\
B<2>b0Ee0Ff5I<3>mQWoVZq_asee<3>xuu cyclerange=3D2/255
}
Lee
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Date: Sun, 26 Apr 1998 17:44:01 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: Re: (fractint) pars of Paul Carlson frms
Gedeon...
>Your incredible output of great formulas continues at a pace I cannot
>keep up with, but by all means keep them coming! As the pars below show,
>I am far behind. I haven't even gotten to any of the midgets yet! The
>pars you posted these past few days are sublime!
>
>Gedeon
Thanks for the comments! The pace is about to slow down for a while.
I made all of the images for your pars - all *very* nice! My favorite
is gp-ibubj-01, really beautiful! Caterpil is cool (if you like crawly
critters).
Paul Carlson
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Date: Sun, 26 Apr 1998 17:54:13 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: Re: (fractint) sprouts
Nice image, Lee! (I thought I saw the ghost of a blue wooly mammoth
hiding behind the sprouts!).
Paul Carlson
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Date: Sun, 26 Apr 1998 16:17:38 -0700
From: "Angela Wilczynski" <wizzle@beachnet.com>
Subject: Re: (fractint) formula tips
Paul and/or Joyce Carlson wrote:
>
>
> There are three methods you can use to locate nice images:
>
> 1. Start plotting one of pars I provided. Then press the 'z'
> key, then the 'F6' key, then the 'F4' key, then 'Enter' twice.
> This will plot the whole Mandelbrot set (and in most cases will
> plot the whole, or nearly the whole, Mset for whatever equation
> is iterated). Chances are, the stalks, balls or whatever the
> 3D-like elements are, will obliterate much of the detail at the
> edges of the set. Try reducing the parameter, usually real(p1),
> that controls the size of the elements until you have some detail
> at the edges of the set. Then zoom into the areas of detail.
> If the elements are too small you can now try increasing the
> parameter that controls their size.
>
>
> Paul Carlson
>
Paul....
I haven't gotten past method 1 yet which is MUCH better than sliced bread!!!
It's just what I've been looking for. I usually start by entering all the
parameters back into the formula so I can see the whole set......this is way
easier. After I play around with the set then I start to fiddle with the
parameters themselves. Superb tip. There are sooooo many useful features in
Fractint......what a great program.
Thanks Paul....and thanks to the Stone Soup Group for thinking of what I wanted
long before I knew I wanted it.
Angela
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Date: Sun, 26 Apr 1998 18:12:38 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: (fractint) Elliptical bailout formula revisited
comment {
My apologies to whoever posted the formula for the elliptical
bailout today - I cut and pasted the formula and forgot to
save the file so I can't credit the author. Anyhow, I used the
ellipse equation and applied my distance-ratio methodoly to it
(or, as someone once said, I "carlsonized" it). Here is the
result. The par "mand_ell_set" shows the whole Mandelbrot set.
The two other pars are zooms of the same area and show the effect
of varying the ellipse real axis parameter.
Paul Carlson
}
frm:Mand_Ellipse {; Copyright (c) Paul W. Carlson, 1998
; real(p1) = ellipse real axis
; imag(p1) = ellipse imag axis
; real(p2) = number of color ranges
; imag(p2) = number of colors in a range
;
z = w = k = iter = range_num = bailout = 0
c = pixel
a = real(p1)
b = imag(p1)
num_ranges = real(p2)
colors_in_range = imag(p2)
colors_in_range_1 = colors_in_range - 1
:
w = w * w + c
;
dist = real(w) * real(w) / a + imag(w) * imag(w) / b
IF (dist > 1)
bailout = 1
index = colors_in_range_1 * (dist - 1) / dist
z = index + range_num * colors_in_range + 1
ENDIF
range_num = range_num + 1
IF (range_num == num_ranges)
range_num = 0
ENDIF
iter = iter + 1
z = z - iter
bailout == 0
}
mand_ell_set { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=mand_ell.frm
formulaname=mand_ellipse passes=t
corners=-3.986284/2.732366/-2.519494/2.519494
params=16/256/2/125
float=y maxiter=256 inside=253 outside=summ
colors=000OOO<60>yyyzzzyyy<60>OOOC0C<60>yVyzVzyVy<60>C0C000<3>000
}
mellipse1 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=mand_ell.frm
formulaname=mand_ellipse passes=t
corners=-1.994336436926/-1.994329835296/4.401086666311e-006/-\
4.401086667012e-006/-1.994329835296/-4.401086667012e-006
params=16/256/2/125
float=y maxiter=1000 inside=253 outside=summ
colors=000OOO<60>yyyzzzyyy<60>OOO00O<60>FFyGGzFFy<60>00O000<3>000
}
mellipse2 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=mand_ell.frm
formulaname=mand_ellipse passes=t
corners=-1.994336436926/-1.994329835296/4.401086666311e-006/-\
4.401086667012e-006/-1.994329835296/-4.401086667012e-006
params=5/256/2/125
float=y maxiter=1000 inside=253 outside=summ
colors=000OOO<60>yyyzzzyyy<60>OOO00O<60>FFyGGzFFy<60>00O000<3>000
}
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Date: Sun, 26 Apr 1998 19:15:21 EDT
From: SKarl52884 <SKarl52884@aol.com>
Subject: (fractint) stringy MandlePond and LightningBolts
Hi There!
It seems to me the strings differ as to where one chooses to look... and color
is often what 'might' mask them. For instance: observe the ' pond ' ... the
strings...the julias...then cycle the color inward and watch as the strings
disappear and reappear in different areas. Its also the same for the julias.
They appear to be every where...then almost gone.
Also in LightningBolts check the difference in the string
formation...more like chainlightning than the usual organized spikey cross. {
This was way down yonder in the claw ...just back of the magnifacation and
you'll see where I started.}
Steve
~~~^~~~^~~~^~~~^~~~^~~~^~~~^~~~^
}
007LillyPond { ; (c) Steve Karl 1997 { unknown map origin }
reset=1960 type=mandel
corners=-1.62425181/-1.62421609/0.00251904875/0.00255475193
params=0.5/0 maxiter=30000
colors=000mJp<77>VCaE7g<39>VCajt_<13>WFaun_<79>VDaVCaWM_<36>_hU
}
001LightningBolts { ; (c) Steve Karl 1997 using andy8.map
reset=1960 type=mandel
corners=-0.0228990105586422/-0.0228989760356715/-0.99903573855411/-0.999\
035712661882 params=0/0 float=y
colors=000H00<7>`00c00d44<13>zzz<3>snNukDsh3qe0<2>kX0aU0<9>I00<8>0003000\
00003005<5>D0KF0MJ0P<3>Q0ZS0`U2cW4d<2>aGhcKieMkgOmiWokYpmbqoesqjusovupwx\
vyzzzyvxwpuvosujqseoqbmpYkoWimOgkMeiKc<2>f8Yd4Wc2U`0S<4>R0IP0GN0GL0C<4>B\
02900700500005<13>00c<15>zzz<2>tpvrmtrjs<10>bEc`BaY8Z<2>R0S<9>203000033<\
14>0cc<15>zzz<15>0c0<14>030000200<2>A00000kkk
}
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Date: Sun, 26 Apr 1998 19:36:03 -0400
From: alex dukay <dukay@interlog.com>
Subject: Re: (fractint) Fractal Chatting
>Felix wrote:
>
> This note on chating makes me think: How many of you are on ICQ?
>
I am...ICQ# 8515817
Alex Dukay
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Date: Sun, 26 Apr 1998 18:46:36 -0500 (CDT)
From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson)
Subject: (fractint) Elliptical bailout Julia formula
comment {
In case you were wondering (you probably weren't) what the
elliptical bailout looks like when applied to a Julia set,
here's an example, using the distance-ratio methodology.
Paul Carlson
}
frm:Julia_Ellipse {; Copyright (c) Paul W. Carlson, 1998
; p1 = Julia set coordinates
; real(p2) = ellipse real axis
; imag(p2) = ellipse imag axis
; real(p3) = number of color ranges
; imag(p3) = number of colors in a range
;
z = iter = range_num = bailout = 0
w = pixel
c = p1
a = real(p2)
b = imag(p2)
num_ranges = real(p3)
colors_in_range = imag(p3)
colors_in_range_1 = colors_in_range - 1
:
w = w * w + c
;
dist = real(w) * real(w) / a + imag(w) * imag(w) / b
IF (dist > 1)
bailout = 1
index = colors_in_range_1 * (dist - 1) / dist
z = index + range_num * colors_in_range + 1
ENDIF
range_num = range_num + 1
IF (range_num == num_ranges)
range_num = 0
ENDIF
iter = iter + 1
z = z - iter
bailout == 0
}
julellipse1 { ; Copyright (c) Paul W. Carlson, 1998
reset=1960 type=formula formulafile=jul_ell.frm
formulaname=julia_ellipse passes=t
corners=-1.856/1.856/-1.392/1.392
params=0.3571035917848349/0.09715187177062035/16/256/8/30
float=y maxiter=500 inside=253 outside=summ
colors=000O00<15>z88<12>O00c40<14>xU0zW0yU0<11>c40aG0<14>xw0z\
z0yw0<11>aG00C4<15>0zR<12>0C40CC<15>0zz<12>0CC00O<14>FFwGGzFF\
w<11>00OSA`<14>eNxfOzeNw<11>I0KO08<15>z0f<12>O08000<12>000O08
}
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Date: Sun, 26 Apr 1998 20:46:12 -0400
From: "Jason Hine" <tumnus@together.net>
Subject: Re: (fractint) self-similarity
>OK, I've seen a lot self-similar areas before but this one continues to
>befuddle me.
If you look carefully, you can find series of features which form a spiral in
your image, though I admit it's a difficult one to see. I have generally found
that spirals that are going to reveal minibrots have two characteristics:
1) The frequency of the features in the spiral will double on a regular basis as
you zoom into the spiral's center, and
2) the amount you have to zoom to see the central minibrot in a self-similar
region is proportional to the amount you had zoomed into the self-similar region
*without* seeing any minibrots.
I should point out that that second point may not be worded in the best way
possible, but in general, if you zoom into the center of a bottomless spiral for
a while, and then start looking in the arm of the spiral for a minibrot, you'll
have to zoom into the arm about as deep again in order to see one... but long
before you see the minibrot, you'll know you're on the right track because the
features (spiral arms) will double in number every so often (#1 above). Hope
this helps... Jason
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Date: Sun, 26 Apr 1998 21:50:09 -0400 (EDT)
From: kragen@pobox.com (Kragen)
Subject: (fractint) Re: your mail
On Tue, 21 Apr 1998, Jiho Kim wrote:
> > Now think about makeing a 16 million color map. Won't that be fun? all I
> > hope is that it comes with a few and not just the default one in 16 million
> > colors. Just a thought.\
>
> How will painting actually work? Are the 16 million color maps? 16MB
> maps don't seem very possible...
Well, I only have about 786,000 pixels on my screen at home; at work, I
have about 2,160,000. So I guarantee I'll never need more than about
two million colors at once :)
How high do you usually set your iteration counts? In the default
coloring mode, there can't be more than itercount+1 colors on the
screen. Usually that's a few hundred, or thousand. You could probably
get creative with coloring modes (by adding yet-unanticipated options
to fractint -- combining 256-way "binary" decomposition with itercount
coloring, or other interesting things)... probably for most of these
you want to define a colormap as some kind of function that takes a few
variables as inputs (bailout angle, iter count, what have you) and
outputs a point in the color cube.
For hand-edited colormaps, you could simply store the steps you'd have
to take in the palette editor to recreate the colormap -- that way,
simple gradients would take up very little storage, as they should.
etc.
16MB (actually 48MB) colormaps don't need to become a reality.
Kragen
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Date: Sun, 26 Apr 1998 19:13:48 -0700
From: "Angela Wilczynski" <wizzle@beachnet.com>
Subject: Re: (fractint) stringy MandlePond and LightningBolts
Steve
Loved the lily pond.....very beautiful and interesting
Angela
SKarl52884 wrote:
>
> Hi There!
> It seems to me the strings differ as to where one chooses to look... and color
> is often what 'might' mask them. For instance: observe the ' pond ' ... the
> strings...the julias...then cycle the color inward and watch as the strings
> disappear and reappear in different areas. Its also the same for the julias.
> They appear to be every where...then almost gone.
> Also in LightningBolts check the difference in the string
> formation...more like chainlightning than the usual organized spikey cross. {
> This was way down yonder in the claw ...just back of the magnifacation and
> you'll see where I started.}
> Steve
> ~~~^~~~^~~~^~~~^~~~^~~~^~~~^~~~^
>
> }
>
> 007LillyPond { ; (c) Steve Karl 1997 { unknown map origin }
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Date: Sun, 26 Apr 1998 20:00:55 -0700 (PDT)
From: Jiho Kim <kimjd@plu.edu>
Subject: (fractint) I'm testing a theory... Forgive this message
=
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Date: Sun, 26 Apr 1998 21:02:22 -0700
From: "Angela Wilczynski" <wizzle@beachnet.com>
Subject: (fractint) Fractal Page Layout
I was wandering thru the Infinite Fractal Loop and came across this page
http://members.aol.com/MKing77043/gallery_4.htm
I just love the layout here......Mark King uses a table with a couple of subtle
colors to create what I think is a very crisp and good looking page. The focus
is on the fractals (where it should be) and there are no distracting stupid web
tricks.
I also came across Les's, Jack Valero's, Earl Hine's pages......as well as other
names I recognized from this list in my random meanderings. All of the pages I
saw were really well done.....way to go Fractinteeers!!!!! One of the constant
criticisms in articles about web style is a reliance on graphics (animation, web
tricks, etc) to overcome lack of site content. All the sites I looked at had
wonderful stuff.....much of it created with Fractint.
At least the web world is a more beautiful place thanks to Fractint
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End of fractint-digest V1 #176
******************************