While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his: "From Outer Space"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/21705B.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
When I initially saw Albrecht's "From Outer Space"
I thought that it had 5-fold symmetry for a minute.
However, there are six arms on the central figure --
and more clearly -- a center hexagon of blue circles
with glowing yellow hazes on a small circular blue
background. The six orange and yellow "hazes" at
the ends of each of the arms remind me of glowing
stellar atmospheres.
A copy of the color map that creates the glowing
hazes (and blue background) is here:
http://tinyurl.com/21705B-map
or:
http://www.emarketingiseasy.com/Albrecht/21705B_map.jpg
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/21705B.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
21705b { ; From_Outer_Space
; Time 0.34.07 1600/1200
; man-sec-newt-zer-mmods
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=cos/exp/exp/sin passes=t
center-mag=-1.08278931330657500/+0.000679771447793\
55/30.94201/1.1324/-90/3.88578058618804789e-016
params=-0.05825983458967864/0.3785210730307932/217\
05.03564960102/25234.2207090221/151024.0204808192/\
384.32768524288/384.00482000595/128.1007683001/256\
.1007683001/256.2007683001 float=y
maxiter=3072 inside=maxiter outside=tdis
logmap=4 periodicity=0 rseed=-2436
colors=n0B00z<78>vv4ww3ww2<2>zz0zz0zy0<77>z40z30z2\
0z20z10z00<9>s07r08q08<3>n0Cm0Dl0E<59>50u40v30w<3>\
00z000
}
==== End of par file ============================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his: "The Twain Shall Meet"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/51765AZ8.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
The mixing of more than one fractal type in Albrecht's
multifractal_10 formula can create fractal shapes
fractalists might not usually run across. This
fractal combines the fractal types:
many-mods, secant, Newton, phoenix and many-mods
a second time.
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/51765AZ8.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
51765AZ8 { ; The_Twain_Shall_Meet
; Time 0.49.45 1600/1200
; mmods-sec-newt-phoen-mmods
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=sqr/exp/exp/sin passes=t
center-mag=+0.53209050020148800/+0.307041785398280\
10/283.836/1/59.9999999999993463/6.364977989115061\
52e-013
params=-0.05825983458967864/0.3785210730307932/517\
65.03595750222/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/128.1007683001/256.\
1007683001/512.1007683001 float=y maxiter=3072
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000LOr<3>_5fc0ce7_jFRoNIzb0zj0000zr0zz1zzC<\
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<3>UnXRm_NlcJkgFfpAazEXwITu
}
==== End of par file ============================
FOTD -- December 03, 2012 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is a harmless scene in the parent fractal that
results when 9 negative parts of Z^(-1.9) are combined with one
negative part of Z^(-9.1) and (1/C) is added on each iteration.
This parent vaguely resembles a three-leaf clover inside a
5-sided area of chaos inside an outer 7-sided figure. A small
minibrot lies on the eastern edge of the field of chaos.
Today's scene lies in a valley of this minibrot.
The name "At the Breaking Point" implies less stress than it
might imply. It is a phrase that came to mind when I shut off
my thinking apparatus.
The rating of a 7 is right at FOTD average, while the calcula-
tion time of 3-1/4 minutes means that little effort will be
expended when the parameter file is calculated.
Be free of all calculation effort! Check the finished image
online at:
<http://www.crosscanpuzzles.com/Archives.html>
And check the hi-def variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The back images may be accessed at:
<http://www.Nahee.com/FOTD/>
The day began with heavy fog here at Fractal Central, but the
fog cleared off during the morning, leading to a sunny afternoon
with a temperature of 59F 15C. The fractal cats enjoyed an
afternoon in the sun. The humans made it through the day with
nothing happening that was worth telling. The next FOTD will be
posted when it is ready.
Until whenever, take care, and mystics tell that the physical
world we observe with our senses is the mere surface of a far
greater incomprehensible multi-dimensional ocean of non-material
spiritual reality. Physicists tell that the physical world we
observe with our senses is a mere subset of a far greater incom-
prehensible multi-dimensional quantum reality, which curiously
is also non-material. Of course, it's all an unlikely coinci-
dence, into which I'm putting far too much significance.
Or is it?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
AtTheBreakingPoint { ; time=0:03:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip
center-mag=+0.8766875323567763/-0.0239258828535604\
1/1.06232e+012/1/-152.5/0 params=-9/-1.9/-1/-9.1/0\
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periodicity=6 mathtolerance=0.05/1
colors=000LTSKSRKSQJRPIQPIPOHONGNMGMLFLKFLKEKJDJID\
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C29B29A18917816615514403302201100UecTdbScaSb`Ra_Q`\
ZQ_ZPZYPZXOYWNXVNWUMVULUT }
frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "Inner Secret"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/56715AB3.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
Albrecht's fractal gives me the feeling that I want
to look closer (zoom in) and see what secrets are
hidden in the central figure.
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/56715AB3.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
56715ab3 { ; Inner_Secret
; Time 0.27.18 1600/1200
; mmods-phoen-newt-sec-spid
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=asin/exp/exp/sin passes=t
center-mag=+0.00082010874916853/+1.264362085302365\
00/57.86304/1/180
params=-0.05825983458967864/0.3785210730307932/567\
15.06595750222/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/128.1007683001/256.\
1007683001/512.1007683001 float=y maxiter=3072
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000LOr<3>_5fc0ce7_jFRoNIzb0zj0000zr0zz1zzC<\
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<3>UnXRm_NlcJkgFfpAazEXwITu
}
==== End of par file ============================
FOTD -- December 02, 2012 (Rating 6)
Fractal visionaries and enthusiasts:
Today's quickie image shows an under-resolved minibrot in the
parent fractal that comes about when 8 parts of Z^(-0.1) are
combined with 0.8 part of straight Z before (1/C) is added on
each iteration.
This parent appears as a small lima bean. When enlarged, this
lima bean becomes an oval-shaped open area with a smooth
perimeter except on the eastern edge, where a small stretch of
mandel buds lies. Today's image lies in this small area of
mandel stuff.
Perhaps the most striking feature in the scene is the wildly
discontinuous iteration bands, which in places appear as angular
patches rather than the expected smoothly curved bands.
A higher maxiter would have fully resolved the central minibrot,
but would also have changed the colors. The rating of an
everyday 6 indicates that I find nothing exceptional in the
image or its colors.
The name "On the Odd Side" has little to do with the image
except to express my feelings toward it.
The calculation time of 9 minutes is more than the image is
worth. Save time by visiting the FOTD web sites.
Avoid calculation by viewing the finished image online at:
<http://www.crosscanpuzzles.com/Archives.html>
And check the hi-def variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The back images are posted at:
<http://www.Nahee.com/FOTD/>
Increasing clouds through the day led to light rain beginning
around sunset. The temperature of 50F 10C felt pretty much
normal for the start of December. The fractal cats, Nico and
Callie, passed the day doing what cats do best. The humans
passed the day doing nothing. The next FOTD will be posted in
the proper time. Until whenever, take care, and mystics tell
us it's impossible for the puny human mind to grasp what's going
on up there, while quantum theorists tell us it's impossible for
the puny human mind to grasp what's going on down there.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
On_the_Odd_Side { ; time=0:09:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=-0.1223958572564503/-0.0168408862844925\
/2.2e+09/1/70/0 params=8/-0.1/0.8/1/0/0/0/0 float=y
maxiter=2750 inside=0 logmap=678 periodicity=6
colors=000E9PFAQGBRHCSIDTJEUKFVLGWMHXNIYOJZNK_ML`M\
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763331tmmrkkqjjpiinhhmgglffjddicchbbfaae``d__bYYaX\
X`WWZVVYUUXTTVRRUQQTPPROO }
frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "Phoenix on Fire"
created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/252341.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
Albrecht's image has a quite strong 3D effect due
to the different depth of focus in our eyes of the
dominant red and blue elements in his image. The
delicate blue lacework seems to be imprisoned by
the blood-red, sharp-edged bands.
The par set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/252341.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
252341 { ; Phoenix on Fire
; Spider, phoenix
; Time 0.17.32
; Fractint Version 2004 Patchlevel 11
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10 function=cos/exp/exp/sin
passes=t
center-mag=0.017473/0.00308737/1.279389/0.8004/80.114682\
5257964537/-5.86499452750839545
params=-0.05825983458967864/0.3785210730307932/80006.325\
64900001/25234.2207090221/151024.0204808192/384.32768524\
288/384.00482000595/128.1007683001/256.1007683001/128.10\
07683001 float=y maxiter=3072 inside=maxiter
logmap=5 periodicity=0 rseed=-2436
colors=200654<2>000400<23>o00q00s00<3>z00<25>C00A00800<3\
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211<21>icNkeOmfP<3>unTwpVxqWzsX<27>875
}
==== End of par file ============================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "Ornaments"
created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/1536143D.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
Albrecht's image has a great variety of shapes and
colors -- all floating on an inky sea. The variety
is the result of combining more than one fractal
type at the same time. For this fractal, Albrecht
used the mandel, secant, bees, phoenix and julia
types.
The par set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/1536143D.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
1536143d { ; Ornaments
; Zoom into 1536143b
; Time 0.25.37 DOS Shell 1600/1200
; mandel-secant-bees-phoenix-julia
; Fractint Version 2004 Patchlevel 11
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=sin/exp/exp/sin passes=t
center-mag=-0.71012896882282740/-0.078504458682040\
03/21838.24/1/75.0000000000001847/-1.0075613954274\
5871e-011
params=-0.05825983458967864/0.3785210730307932/213\
64.64595712822/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/256.1007683001/512.\
1007683001/768.1007683001 float=y maxiter=3071
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\
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}
==== End of par file ============================
FOTD -- November 30, 2012 (Rating 7)
Fractal visionaries and enthusiasts:
Early in their fractal explorations, beginning fractalists
discover that the higher dimensional fractals hold little of
interest. To put it bluntly, the images all look the same. But
to disprove a point, I present today's image, which lies in the
very narrow ring of interest at the western edge of the
Z^(100)+C Mandeloid.
The unexpected action was created by calculating the image with
the 'exp' function applied to initial C. This slight addition
changed the entire nature of the image. Instead of a screen
filled with similar minibrots, we have an interesting assortment
of effects, including a vertical range of resolution, from near
perfect at the top to total breakdown at the bottom. Curiously,
though the large scale breakup is quite obvious, the small-scale
edges of the breaks are well resolved.
The lower half of the image in particular has an art-deco
feeling about it. The name "Art-Deco Breakup" refers to this
resemblance. The rating of a 7 is FOTD average. The
calculation time of 1-1/3 minutes is also near average.
The finished image is online at:
<http://www.crosscanpuzzles.com/Archives.html>
High-def variations are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The FOTD back images may be accessed at:
<http://www.Nahee.com/FOTD/>
A mix of sun and clouds with a temperature of 43F +6C made today
the latest in a string of similar days here at Fractal Central.
The fractal cats passed the day watching the outside conditions
as well as each other. The humans did a lot less watching and
notably more working. The next FOTD fractal will be posted
around December 2.
Until whenever, take care, and pseudoscientific occultists claim
there are higher-dimensional realities they call astral planes.
Totally scientific physicists claim there are higher dimensional
realities they call parallel alternate universes. As for me,
I'm waiting to see some kind of solid proof that any of these
invisible worlds actually exist. (Of course, by definition they
are invisible, so how can anyone find solid proof?)
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Art-Deco_Breakup { ; time=0:01:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotFNC function=exp passes=t
center-mag=-34.2/0/0.3267943/1/90/0 params=100/0/0\
/0/-1.007026054383232/0 logmap=9 maxiter=1800
inside=0 float=y periodicity=0 mathtolerance=0.05/1
colors=000B8s9Br8Er6Hq5Kp4NpDQnKWlVdjcohYigTdfOZeJ\
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mOG2RA3hVT`X`TZgL`nEbuCYt }
frm:MandelbrotFNC {; Jim Muth
b=p1, z=p2, c=p3+fn1(pixel):
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "Mandel Invasion"
created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/2022201.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
The "marching Mandeloids," crackling with
electricity, seem to be colliding in the
center. The red, blue, silver and gold color
map appears to be similar to the one used
in yesterday's fractal.
The par set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/2022201.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
2022201 { ; Mandel_Invasion
; Time 0.02.37 1600/1200
; 4*mandel
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=exp/exp/exp/sin passes=t
center-mag=-0.491807/5.55112e-016/0.9752988
params=-0.05825983458967864/0.3785210730307932/202\
22.32595710666/25234.4911020602/151024.0204808192/\
384.32768524288/384.00482000595/128.1007680001/512\
.10076800005/768.10076800002 float=y
maxiter=1024 inside=maxiter logmap=4
periodicity=0 rseed=-2436
colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A9\
6875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\
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2<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>86\
4
}
==== End of par file ============================
FOTD -- November 29, 2012 (Rating ?)
Fractal visionaries and enthusiasts:
The FOTD is currently being posted every other day. This is due
to an unusually busy spell here at FC. After the holidays, the
FOTD will return to its almost-every-day schedule.
Today's image shows what a person would see surrounding him if
he stationed himself at the center of a Julia spiral. (In this
case, the spiral is one of those associated with Seahorse Valley
of the Mandelbrot set.) As he looked around, he would see a
wall of rings in all directions. If his view were unwrapped and
projected onto a flat screen, it would appear as today's image,
which is part of a periodic larger image. This larger image is
periodic because the 'exp' function shows what he would see if
he continued rotating his view indefinitely.
Don't shuffle the kids away. The name "Kinky Corner" refers to
the small kink in the lower left corner.
The image has been stretched about three times in the vertical
direction to make the straightened-out spiral arms more apparent.
Since the interest is purely mathematical, I could not give the
image a rating. The question mark indicates the uncertainty.
Unfortunately for those with limited time, the image is a slow
one, taking 11 minutes to finish. The good news is that the web
sites are there to make fractal life easier.
The image may be viewed without the need to calculate it by
visiting the official FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
Variations are posted in high-definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The FOTD back images are at:
<http://www.Nahee.com/FOTD/>
Cloudy periods alternated with sunny periods here at Fractal
Central today, while the temperature of 43F +6C was close to
normal. The fractal cats had an average day of it, as did the
humans. The next FOTD will be posted in a day or two.
Until whenever, take care, and which is more likely to be in two
different places at the same time, a Christian saint in a state
of bilocation or an electron in its wave aspect? (Both things
are apparently impossible, yet both are claimed to be true.)
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Kinky_Corner { ; time=0:11:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=slices.frm
formulaname=JuliaFNZ function=exp passes=1
center-mag=-5.62965/12.738/0.5560629/0.3862/-95/0
params=2/0/-0.5010419796557/0.0152933866127/-0.751\
85195471/0.030619434187 float=y maxiter=2450
inside=0 logmap=-777 periodicity=0
colors=0000Xd0Ye0Zf0_g0`h0ai1bj2ck3dl4em5fn6go7hp8\
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CUDCVDCWCBXBBZBB_AB`9Ba9B }
frm:JuliaFNZ {; Jim Muth
b=p1, z=p2+fn1(pixel), c=p3:
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
