FOTD -- December 03, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
Due to a minor rush here at FC on Thursday, the day I work on
Friday's FOTD's, the discussion will be on the brief side.
Today's image is an unperturbed view of the area of yesterday's
image. I named it "Mandelbrot Eruption" because of the detail
that suddenly erupted inside the central Julia-type feature as
I raised the maxiter beyond 33,000.
Actually, I'm not sure the Julia thing is actually a Julia
thing at all. It certainly is no minibrot, nor does it resemble
any Seahorse or East Valley type Julia set that I have come
across. Of course, I have checked only an infinitesimal part of
the total number of possible Z^2+C East-and-Seahorse type Julia
sets.
The rating of a 6 indicates a modest amount of artistic worth in
addition to the mathematical interest.
The calculation time of 54 seconds will demand no patience at
all. Simply copy this entire letter into the Fractint directory
(folder), in text mode, with a *.par extension, and run it as
you would any other parameter file.
And if Paul's recovery is on schedule, the finished image
already is or soon will be available on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Scudding clouds, brisk winds and a temperature of 36F +2C
brought the feeling of winter to the Fractal Central area on
Thursday. The fractal cats would have preferred more sun, but
were reasonably happy by the heat. With the work backup cleared
away, my day was satisfactorily busy. The next FOTD will be
posted in 24 hours. Until then, take care, and I lean toward
conservative views, and I think we're fighting for freedom, but
I always wonder what it is that we're fighting to be free from.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
MandelbrotEruption { ; time=0:00:54.54-SF5 on P4-2000
reset=2004 type=mandel center-mag=+0.2985719667698\
861/-0.01848742851637421/2.480859e+012/1/155/0
params=0/0 float=y maxiter=33225 inside=0
outside=summ periodicity=0 mathtolerance=0.05/1
colors=000mGNkGLiGJgHHeHFcHDbHCg3qd4rb5r`5rZ6rX6rV\
7rT8rR8rP9rN9rLArJBrHBrFCrDCrBGsAKs9Os8St7Vt6Zt5bu\
4fu3iu7frAcoD`mHYjKWhNTeQQbUN`XKY_IWbFTfCQi9Ol6Lo4\
JTHC6T5L`BZgGloLzvQzuHuzVzzhhzgzzfOzezzd3zczzc4Ic5\
Jc6Jb6Jbzzb7zbzza9zazzaAzazzazz`Cz`Cz`DM`DM_EN_FN_\
FN_GNZGOZHOZIOZIPZJPYJPYKPYLQYLQXMQXMQXNRXORWORWPS\
WPSWQSWRSVRTVSTVSTVTTUUUUUUUVUUVUUWTTWSTWRTWQSWPSW\
PSWOSWNRWMRWLRWKQWKQWJQWIQWHPWGPWFPWFPWEOWDOWCOWBN\
WANWANW9NW8MW7MW6MW5LW5LW4LW3LW2KW1KW0KW0KY0LZ0M_0\
N`0Oa0Ob0Pc0Qd0Re0Rf0Sg0Th0Ui0Uj0Vl0Wm0Xn0Xo0Yp0Zq\
0_r0_s0`t0au0bv0bw0cx0dy0ez0ew2au3Ys5Uq6Qo7Mm9IkAE\
iCAgD6eE2cG7aIB`KFZMJXONWQRUSVSUZRWbPYfN_jManKcrJd\
vIcuIbtHat00L00M00N00O10P20Q30R40S50T60U70V70W60X6\
0Y60Z50_50`40a40b30c30d41e52f63f64e65e56d57c48c49b\
4Ab3Ba3C`2D`2D_1C_1BZ1BZ2F`3Ia4Mc5Pd5Se6Wg7Zh8bj9e\
k9hlAlnBooCsqDvrDysFwqoGP }
END PARAMETER FILE=========================================
FOTD -- December 02, 2010 (No Rating)
Fractal visionaries and enthusiasts:
Due to a power failure at FC on Wednesday, today's image is a
slow one that only the stout-hearted will care to calculate.
With the electric power out all morning and the work backed up
all afternoon, I had no time to do a fractal search. But I did
have a spare fractal in readiness. After I posted yesterday's
FOTD, I checked the object at the center of that image. Since
the resulting fractal took over an hour to finish, I did not
intend it to be an FOTD, but the fates determined that the
fractal should indeed be today's FOTD.
The object at the center of today's image exists in a perturbed
Mandelbrot plane. I leave it to the viewer to decide what kind
of a thing it is.
Since the image was never intended to be a FOTD, I could not
rate it.
The name "Weird Julibrot Set" fairly describes the image.
The calculation time of over one hour on my 2000mhz machine will
separate the fractal professionals from the fractal amateurs.
The pros will run the included parameter file and wait it out.
The amateurs will shrug and say, "I'm not really that interested
in the image."
If Paul is feeling well enough, both pros and tyros may find
time relief on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
where the finished image could be posted.
Wednesday began with steady rain and a temperature of 63F 17C
here at Fractal Central. Around 10am a fierce squall arrived
with torrential rain and winds of 55mph 88kph. When the excite-
ment ended, the lights were out, the fractal basement had taken
on water and the temperature was down to 39F +4C.
Most of the rest of the day was spent waiting for the lights to
come back on and getting the work caught up, while the fractal
cats wondered what all the excitement was about. The next FOTD
will be posted in 24 hours. Until then, take care, and how can
the belief in karma be true if we live on earth only once?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Weird_Julibrot_Set { ; time=1:01:07.20-SF5 on P4-2000
reset=2004 type=mandel center-mag=+0.2985719666083\
7880/-0.01848742792247442/1.529455e+011/1/142.5/0
params=0.3101057985168/0.8009060914945 float=y
maxiter=24000 inside=0 outside=tdis periodicity=6
colors=000JaLJ`MJ_NI_OIZPHYQHXRGXSGWTGVUFUVFUWETXE\
SYESZGT_IT`KUaLUbNUcPVcQVdSWeUWfWWgXXgZXh`XiaYjcYk\
eZkgZlhZmj_nl_om_oYXdJVUMUVOTVQTVSSVVSVXRWZRW`QWcP\
WePWgOXiOXlNXnNXpMXrMXiNP`OHSP9JQ2KR3KR3KR4KR4KR5K\
S5KS6KS6KS7KS7KS7JS7JS8JS8IS8IS8HS80S9Yv_Yu_gzehzd\
izckzblzamz`nz`kzaizbgzcezdczeaxf_vfYtgWrhUpiSnjQl\
kOjlMhlKfmIdnGboE`pCZqAXr8WrEXpJYoOYmTZlYZkc_ih`hm\
`fraewadv`eu`ft`gs_hr_ir_jqZkpZloZm50650750850950A\
50C50D50D60F70F60H50I60I50I40H31J22J11I02K02H53QA4\
NF6RJ7WO9_SBcVDhZElbHpeJtfMrfNqfPpgPngRlgRjhThhUfh\
VdhWbiX`iYZiZWj_Uj`SjaQjaOkbMkbKkcIlcGldEldCleAkfB\
jgBihBhjBglCgnCfpCerGdtKcvPcxUhzZmzcmzemzgmzivzkzz\
mzzozzqzzszzuzzsrzrhzqZzpPyoMvnmsmcplmnkcljmjichjU\
fkcdlcbmZ`mZemcmpUgtUbsUerSXrQXqOWpMWpKVnIVmGUlEUk\
CUjATiATgATfBSeCSdCRcDRbER`EP_FOZFNYGMXHLWHKUIJTJJ\
SJIRKIQKIPMmzmdzLmzKbJKbK }
END PARAMETER FILE=========================================
FOTD -- December 01, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is obviously a Seahorse-Valley type Julia set. So
what then is it doing in one of the perturbed Mandelbrot sets,
where it is surrounded by pieces of East Valley elephants?
Actually, it's no mystery at all. The Julia shapes are univer-
sal in all orientations of the 4-D Julibrot. The Mandelbrot
shapes are special however, existing in their pure form only in
the Mandelbrot planes, which are defined by real and imag 'C'.
Today's seahorse Julia shape is surrounded by elephants because
the perturbed scene is located at the 'C' coordinates of
Seahorse Valley of a minibrot that lies in East Valley of the
Mandelbrot set. The name "Seahorse Elephants" describes this
relation.
I found the image by first zooming deep into the Seahorse Valley
of the largest Minibrot in the radical complex of the period-14
elephant on the southern side of East Valley of the M-set.
Then, by using the evolver feature of Fractint, I found a per-
turbed value of Z where a chaotic area overlies the minibrot's
Seahorse Valley.
The holes in this overlying layer appear as variations of the
shape of the Julia set of whatever part of the Mandelbrot valley
lies directly beneath them. And the image holds some Julia-type
figures that are even more interesting. For more craziness,
increase the maxiter and check the small but twisted set at the
center of today's image.
The rating of a 7 is what I think the image is worth. But I do
not think the image is worth the 11-1/2 minutes it will take to
finish the calculation. To get a quick glimpse of the general
shape, I suggest changing the outside from 'tdis' to 'iter' and
setting the logmap to negative 215, which will shift the calcula-
tion to machine language and cut the calculation time to a few
seconds.
I rendered the image with the outside set to 'tdis' because this
spreads the colors in the best manner. When the outside is set
to 'iter' or any of the 'real' family, (real, iter, mult, summ),
the color bands are either too narrow, giving a totally chaotic
effect, or too broad, giving too many boringly flat areas.
The way to see the full craziness is to muster your patience and
run the included parameter file, or to try the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Even with a mild temperature of 59F 15C, the heavy clouds and
steady rain here at Fractal Central on Tuesday made things less
than ideal for both man and cats. The cats missed their sun,
while the man wanted the work finished. The cats got no sun,
though, with some help from FL, the man did manage to get the
work finished. The FOTD fractal soon followed.
And speaking of fractals, the next one will be posted in 24
hours. Until then, take care, and give homage where it is due.
I leave it to the individual to decide where homage is due.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Seahorse_Elephants { ; time=0:11:33.63-SF5 on P4-2000
reset=2004 type=mandel center-mag=+0.2985719666032\
641/-0.01848742793131565/7.471066e+009/1/142.5/0
params=0.3101057985168/0.8009060914945 float=y
maxiter=12000 inside=0 outside=tdis periodicity=6
colors=000gzehzdizckzblzamz`nz`kzaizbgzcezdczeaxf_\
vfYtgWrhUpiSnjQlkOjlMhlKfmIdnGboE`pCZqAXr8WrEXpJYo\
OYmTZlYZkc_ih`hm`fraewadv`eu`ft`gs_hr_ir_jqZkpZloZ\
m50B50C50D50E50F50H50I50I60K70K70K70N60P50Q40R31S2\
2O11N02L02K53OA4RF6UJ7YO9`SBcVDhZElbHpeJtfMrfNqfPp\
gPngRlgRjhThhUfhVdhWbiX`iYZiZWj_Uj`SjaQjaOkbMkbKkc\
IlcGldEldCleAkfBjgBihBhjBglCgnCfpCerGdtKcvPcxUhzZm\
zcmzemzgmzivzkzzmzzozzqzzszzuzzsrzrhzqZzpPyoMvnmsm\
cplmnkcljmjichjUfkcdlcbmZ`mZemcmpUgtUbsUerSXrQXqOW\
pMWpKVnIVmGUlEUkCUjATiATgATfBSeCSdCRcDRbER`EQ_FQZF\
QYGPXHPWHOUIOTJOSJNRKNQKNPMeGLdHLcIKbJKbKJaLJ`MJ_N\
I_OIZPHYQHXRGXSGWTGVUFUVFUWETXESYESZGT_IT`KUaLUbNU\
cPVcQVdSWeUWfWWgXXgZXh`XiaYjcYkeZkgZlhZmj_nl_om_oY\
XdJVUMUVOTVQTVSSVVSVXRWZRW`QWcPWePWgOXiOXlNXnNXpMX\
rMXiNP`OHSP9JQ2KR3KR3KR4KR4KR5KS5KS6KS6KS7KS7KS7JS\
7JS8JS8IS8IS8HS80S9Yv_Yu_ }
END PARAMETER FILE=========================================
FOTD -- November 30, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
With more than average graphic design work to be done on Monday,
today's discussion will have fewer than the average number of
words.
Today's 6-rated image is part of the same 'fan' that produced
yesterday's 8-rated image. The scene is located on the fringe
curving out from the bottom right edge of the fan.
The name "Fractal Boogie-Woogie" came to me when something about
the image reminded me of that 8/4 rhythm.
If I had had more time to work on the colors, the image might
have earned a higher rating. As it is, the rating of a 6 will
have to suffice.
The image is rather slow, taking over 23 minutes to finish.
Those who have too little time to spare may try checking the
FOTD web site at:
<http://www.Nahee.com/FOTD/>
to see if it is up to date yet.
A mixture of sun and clouds, with a temperature that rose from
21F -6C to 46F +8C made Monday notably fall-like here at Fractal
Central. The cats of the fractal variety, (as all cats are),
spent most of the afternoon on their window shelf, stretching
out when the sun appeared and curling up when it went behind a
cloud.
My day was busier than average. (There's been a lot of that
going around lately.) The next FOTD will be posted in 24 hours.
Until then, take care, and this is the one and only genuine
FOTD. Accept no substitutes.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
FractlBoogieWoogie { ; time=0:23:20.60-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+0.5902872895/-2.3048310835/37539.65/1/\
170.2/0 params=-22/-1.1/-5.5/-11/0/574/0/0 float=y
maxiter=18000 inside=0 logmap=794 periodicity=6
colors=00095CD7EGAFKEHNIIRLKUPLYTM`WOd_PgcRkfSnjUr\
nVuqWttXtrXspXsnXrlXrjXqhXqfXpdXpbXo`XoZXnXXnVXmTX\
mRXlPXlNXkLXkJXjKYiKYhKYgLZfLZeLZdLZeK_fJ`gIahHbiG\
cjFdkFelEfmDgnChnBioAjp9kq8lr7ms6nt5ou4pv3qw2rw1rs\
0np0jm2fj4ch6bf7be9bcAbbCb`DbZEaYGaWHaVJaTKaSLaQN`\
OO`NQ`LR`KT`IU`GV_FX_DY_C__A`_9a_EU`JN`NFaS8aW1aZ2\
Y`4Tb6Pd8Kg9GiBBkD7mE3lC6kB9jACi9Fh8Ig6Lf5Oe4Rd3Uc\
2Xb3Ua4R`5P_6MZ7KY8HX9EWACVB9UC7TD4TE2RG5QI7PKAOMC\
MOFLQHKSKJTMHVPGXRFZUE`WXEQzy`zyczyezTjzEoz0sz1kz2\
cz3Xz4Pz5Hz5Az6Ez7Hz7Kz8Nr8QU9Tz9WzAZzBazBdzCgzCj`\
DmaDpZEYTEXcKocQicTccTXcTRcTLaTKWJJWYzUYzVYzVYzVYz\
VYzVYzVYzVYzWYzWYzWYzWYzWYzWYzWYzWbzZbz`bzbbzdbzfb\
zhbzibzjbzjbzkbzkbzlbzlbzmbzmbzhozcoz_ozVozQozMozH\
ozCoz8oz8oz8oz8oz8oz7oz7oz7ozmtzmtzmtzmtzmtzmtzmtz\
mtzutzutzutzutzutzutzutzutzztzztzztzztzztzztzztzzt\
zztzztzztzztzztzztzztzztz }
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=========================================
FOTD -- November 29, 2010 (Rating 8)
Fractal visionaries and enthusiasts:
Today we stay with the same fan that appeared in the image of
two days ago, but instead of delving into the edge of the blade,
we have checked the handle. What we find there is a curious
kind of bud with a filament extending into a kind of 'star'.
Today's image lies near the point where the filament terminates
at the center of the star.
I named the image "Fanning Out" because instead of concentrating
on the fan blade, we are broadening our horizon to include the
handle of the fan.
The rating of an 8 shows that by broadening our horizon we have
found a better image. The calculation time of under 5 minutes
is slower that what I consider ideal, but the image that will
appear makes it all worth the effort.
And if Paul is still on the road to recovery, the finished image
will soon be available on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Morning clouds, afternoon sun and a temperature of 43F +6C made
Sunday a rather pleasant day here at Fractal Central. The
fractal cats, being cats, passed the sunny afternoon on their
shelf in the southwest window, keeping comfortably warm. My day
was uneventful. The next FOTD will be posted in 24 hours.
Until then, take care, and I hear that in 50 years, technology
will have solved all our problems, including global warming. If
anyone doubts this, all they need do is ask those in snowbound
Europe how worried they are about global warming right now.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Fanning_Out { ; time=0:04:52.92-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+0.235409017246/-0.00349153665/5.6e+008\
/1/141/0 params=-22/-1.1/-5.5/-11/0/525/0/0 float=y
maxiter=3600 inside=0 logmap=-560 periodicity=6
colors=000000HE7ED7BB88A958A37A59C7AD9BFBCGDCIFCJH\
DLJDMLDONEQPFSRGUTHWXFY`9_c3_jF_nR_qbQwnGwz7sv8qs8\
gp8gm9fi9ff9ecAe`AdXAdUBcRBcOAhNAmMArMAoMAlMAiIAfF\
AcCAa9A_4AY0AX3AT6AQ8AO9JMAGLBKN1OQFKWIFaOBgU6mW2r\
Y6vZAz`EvaIrcSmdchfrcgvZizUjzPmzKozIrzFuzIxzMzzPzz\
RzTTzzUzTmwzXtTZqz_nUakzbjUNYP6L0EN0LP0SR0_T0mVqrX\
svZuzYszYrzXqzXozXnrWmjWliWjgVifVheVfcUebUdaUcXV_S\
WWOXSJYOEZKAZGEcIHhJLmKOqLWfMcWNjMOrBPy1Pz4Uz7VzAY\
zD_zGbzJezMgzPjzSmzVozYrz`uzcwvcvrcvncvkhvgivcjv`k\
vXlvTmvQnvMovIpvFqvHorJmoLklNjhPheRfbSe_UcWWaTY_Q_\
ZMaXJcVGdUDhYIlaMpdQleThfVegYah_ZiaVidSjfOkhLlkHmm\
EmoHnmKolNpjQqiSrgVsfYte`uccvbew`hx_kyYnzXpzWozVoz\
VozVozVozVozVozVozUozUozUozUozUozUozUozUmzWkzYiz_h\
zafzcdzdczfazh_zjZzlXzmVzoUzqSzsQzuPzwqzxnzylzzjzz\
hzzezzczzazz_zzXzzVzzTzzRzzSzzUzzWzzXzzZzz`zzazzcz\
zdzzazzZzzWzzTzzQzzNzzKzz }
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=========================================
FOTD -- November 28, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Yesterday's image showed one of the frequently mentioned but
rarely seen fractal 'fans' that exist in fractals of the type
(-n*(Z^-n))+(-n*(Z^-n))+(1/C). Today we check one of the
minibrots that exist around the edges of such fans.
In today's image we doubled the (Z) portions of the FOTD of
November 23. The resulting parent fractal closely resembles the
earlier image, though its size is slightly smaller.
Today's image is located on the right edge of the 'fan' that was
featured in yesterday's image. The overall effect is of a
minibrot in one of the higher-order 'stars' of the Mandelbrot
set. There are also minibrots all over the flat 'blade' of the
parent fan, though it takes a bit of searching to find them.
The name "Near the Optimum" is misleading. I see nothing in the
image to imply that something in it is near optimum. In fact, I
doubt that anything in fractals can be considered at optimum,
except perhaps for a critical value for initial Z in certain
fractals.
The rating of only a 7 means that calculation time of 16-1/2
minutes will be more effort than the result will be worth.
The finished image is or soon will be posted on the FOTD web
site at:
<http://www.Nahee.com/FOTD/>
If the image is not yet posted, be patient. Paul is doing his
best to get the FOTD site caught up, but he is still recovering,
and it might be a while before things are completely back to normal.
Saturday brought snow flurries, but with some afternoon sun, and
a temperature of 39F +4C to Fractal Central. The snow flakes
brought the fractal cats to the window, but they soon grew bored
and returned to warmer spots.
My day was average. The next FOTD will be posted in 24 hours.
Until then, take care, and if we could change the past, would we
know the future?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Near_the_Optimum { ; time=0:16:32.05-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip float=y
center-mag=+1.934869010826633/-1.863451620247872/\
1.059113e+010/1/-167.5/0 params=-22/-1.1/-5.5/-11\
/0/525/0/0 maxiter=12000 inside=255
logmap=2000 periodicity=6
colors=000UGVXKSZOP`RMcVJeTGgXDiVBa_PUWbMSoPUmRVlU\
WjWXiZYh`Zfc_ee`chabjYamc_cQZmWXcUWgYV9APD0dH0bL4`\
P8ZTDYXHW`MUdQShVRlZPkcNjYLiXKiTMhYMhTMhYMcYMZYMUY\
MPYMKYMFYMRXGbRBH0FSP1bHIbJZRCnPBlNAkLAiJ9hH9fF8eD\
7cB7b96`76_89a8Bc9De9Fg9HiCIgFJeHKdKKbNLaPM_SMZUNX\
XOW_OUaPTdQRfQQgRRgRRhSRhSRiTRiTRjURjURkVRkVRlWRlW\
RmXRmXRbVRSTRTRVTQYTOaUNdUMhUKkVJoVHrVGvVFyUCYUA79\
UwBSvCQvDOuEMuFKtGItHGtJEsKCsLArM8rN6qO4qP2qhL6eN7\
cP8aR9VIJPASQBRRCQSDPTEOUFNVGMWGLXHKYIJZJI_KH`LGaL\
FVGDPBBI69C27D6AGACJEFKIHMJKOLMPOPVmRXbUZgW`lZbq`b\
vbakd`_e_RfZIgZAhWCgTEgSGgQIgPKgNMgMOgRQeWTc`VaeY_\
j`YubczeUxgSwiOvkLzzItnFzsCrzzzz6pwcztzlqEznGhlzzk\
LTdzpjNbigjhSZgUffXVeZXfcWgbWhbWibWjbVkbVlaVmaVmaU\
maUmaUmaUm`Tm`Tm`Tm`Tm`CmoDmnEmzFmzGmzHmzImzJmzKmz\
PmzUmzZmzcmzhmzmmzmmzmmzmmzmmzmrzmrzmrzmrzmrzmrzmr\
zmrzmrzmrzmrzmrzmrzmrzzzz }
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=========================================
FOTD -- November 27, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
In many fractals of today's double-negative type, I tell of a
prominent 'fan' in the parent fractal. Until now however, I
have been pretty much ignoring this 'fan'. In today's image
this oversight has been corrected.
The image shows one of these 'fans' in its full glory. The
handle of the fan is at the origin of the fractal, while the
blade points directly east. Today's image has been rotated 90
degrees, so that the blade points straight up instead of to the
right.
Minibrots abound in these fans, especially along the edges,
though sometimes they are difficult to find. Quite a few mini-
brots are buried in today's image, and I just might find a few
of them and turn them into the FOTD's of the next few days.
The name "The Great Fan" says it all. The rating of a 7 makes
the task of running the parameter file a minor one, especially
since the image finishes in a lightning-fast 23 seconds.
The finished image is or soon will be available on the FOTD web
site at:
<http://www.Nahee.com/FOTD/>
Morning clouds cleared away for afternoon sun here at Fractal
Central on Friday. The temperature of 39F +4C and brisk winds
kept things chilly, but were nothing that would be considered
exceptional in late November. The fractal cats kept snug on
their shelf in the strong afternoon sun.
With the work caught up and the holiday past, my day was relax-
ing. The next FOTD will be posted in 24 hours. Until then,
take care, and when the truth shines through the fog, will it be
recognized even if it proves to be irrational, or is irrational
truth an absurdity?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
The_Great_Fan { ; time=0:00:23.12-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip float=y
center-mag=1.578/0/0.4/1/90/0 params=-22/-1.1/-5.5\
/-11/0/525/0/0 maxiter=1500 inside=0 periodicity=6
colors=0009BcCAc98bU6b95bc3bA2bcDc88dmFd6DerKf3Ifv\
Pg3OhzWh6Tiz_j4Yjzak2clzcl3dkzej0dizeh0dgyef0dexed\
0dcwfc0ebuha0gasj`0i_qk_0kaolb0mcmndKofipgcqherics\
katl_umYvnWwpUxqSyrQzsOvpMrmLnjJjgHfdGbaEZZDVWBRT9\
OQBQQDSRFURHWSJYSL_TNaTPeUSgUViVYkV`mWcoXfqYhsWhtT\
hsQhrNirKiqHipEipBjoAjnAjnAjmAkmAklAklAkkAkkAkkAUj\
CBhDAfE9dF8bG8`H7ZI6XJ6VK5UL4SM4QN3OO2MP2KQ1IR0GS0\
FTDJPPNLaRHmVDyZ9wYAuXBsWCrVDpVEnUFmTGkSHiSIhRJfQK\
dPLcPMbRObSPaTQaUR`VS`WT_XU_YVZZWZ_XY`YYaZYb_Va`Ta\
`R``P``N_aL_aIZaGZaEYbCYbAXb8Xb6Xb5Vd5Tf4Sg4Qi3Ok3\
Nl7RmAUmEXmH_mLbmOemShmVkmZnmaqmWefRV`MJVH8PH8PG8O\
G8OG8OF8NF8NF8MF8ME8ME8LE8LD8LD8KD8KA8HC8KC8JC8JB8\
JB8IB8IA8IA8HA8HGdVFcUFcUFbUFbUFaUFaTF`TF`TF_TF_TF\
ZSFZSEZSEYSEYSEXREXREWREWREVREVQEUQEUQEUQDTQDTPDSP\
DSPDRPDRPDQODQODPODPODOODOOCONCNNCNNCMNCMNCLMCLMCK\
MCKMCJMCJLCJLBILBILBHLBHK }
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=========================================
FOTD -- November 26, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Things were rather busy here at FC on Thursday, which was the
holiday on which we give thanks for something I'm not quite
sure of. But despite the activity I found time to locate a
worthy fractal.
I took the parent fractal of three days ago and cut the portions
in half. The effect was to do little more than double the size
of the parent.
Instead of lying in a valley at the southern edge of the 'fan'
of the parent, today's scene lies in a spiralling filament
extending from a twisted minibrot on the southeastern edge of
the fan.
The name "Spiral for the Ages" is admittedly overblown. The
chief feature in the image is the minibrot, not a spiral. The
rating of a 7 is about what the scene is worth. If I had more
time, I might have improved the colors and raised the rating a
half point or so.
The image calculates in just one minute -- in the super-fast
category. No time will have been wasted if disappointment
prevails after the minute. And the image is always available on
the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Thursday began with snow and sleet here at Fractal Central. For
a while it looked like a white Thanksgiving was in store, but by
late morning it all changed to rain and within an hour the centi-
meter or so of snow that had piled up was gone. The fractal
cats kept careful watch on the big floppy flakes for an hour or
so, then decided to ask for food. The temperature rose during
the day from 32F 0C at daybreak to 39F +4C at nightfall.
My day was pleasant enough. FL kept the two guests who were
expected well supplied with food, while the foul weather kept
any unexpected visitors from dropping by. The next FOTD will be
posted in 24 hours. Until then, take care, and what will the
next media-manufactured crisis be? It's already got me worried.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Spiral_for_theAges { ; time=0:01:03.44-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip float=y
center-mag=+4.21799657059/-4.05052923939/1.92e+007\
/1/100/0 params=-5.5/-1.1/-0.55/-11/0/525/0/0
maxiter=1500 inside=0 logmap=135 periodicity=6
colors=000dsmbtmcrm`umZtmYvmVvmTwmRymTxmUwmWvmXumY\
tm_sm`rmaqmcpmdomfnmgmmaUmjkm_SmlimYQjifmWOgfckUMd\
c`iSKa_YhQIZWUfOGWSQcMETOM_KCQKIXIANGEVEBKCAPA8H86\
F04F02050A40C30B20D10F50IA0HF0GK4EP8CUCAZDAcEAhFAm\
FArKAvPAwUCwZEwZGwZGwcGwhFwhEwmGwmHwrJwrKwwLwwNssO\
ptQmpRjlSggUddVccWc_YcTZcU`cVacWbcXdeYefZfdZeb_d`_\
cZ_bX_bV_aT_`R__P__N_ZL_YJ_XH_XF_WD_VB_U9_U7_T5_S3\
_R2_R6YL9WGCUAFS5IQ0HO4HN8GMBGLFFLIFLMFLPJUQM_QP`Q\
SXQVZQYVQ`WQcSQfUQiVQlWQoXQrYQp_Sn`TlaUjTVhVWfWXeX\
YcY_a_`_`aYabWbcUcdTceRcgPchNciLcjJckHclGcmEcoCZpA\
Zq8Zr6Zs4Zt3Zu2Zs2Zr2Wq2Ro2Jn2Bm23l64m95nC6oF6pJ7q\
M9rP9rSBsWCtZDuaEvdGwgGwhJxhKxiMxiNxjPxjQxjSxkTxkV\
xlWxlXxlZxm_xmaxnbyndyoeyogyohypiypkzqlzqnzqozrqzr\
rzsszstzsuztvzuwzvxzwyzxzzyzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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=========================================
FOTD -- November 25, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
The FOTD is late. The reason -- I was too busy with other
things on Wednesday Nov. 24 to do a proper search for the image
for Nov. 25.
Today's image is named "Mount Mountain", a fine name for a
fractal mountain if ever there was one. The mountain exists
mostly in the human mind, though partly in the parent fractal
that is created when the formula Z^(1.1)+C is iterated 11 levels
up the multi-dimensional complex logarithmic hyperladder with no
function applied to the works.
I rated the image at a 7, which is not too bad for a fractal
mountain with a touch of snow on its peak.
The calculation time of 12-3/4 minutes is admittedly slow, but
then good things are worth waiting for, and the calculation can
always be bypassed by going direct to the finished image on the
FOTD web site at:
<http://www.Nahee.com/FOTD/>
Sun in the morning gave way to clouds in the afternoon here at
Fractal Central on Wednesday, while the temperature reached no
higher than a chilly 45F +7C. The fractal cats spent most of
the day watching their television, which is what they see on the
other side of the window when they sit on their shelf.
My day was occupied getting the work caught up before the big
holiday. FL busied herself picking up the goodies for the
Thanksgiving feast. If we're lucky, only two guests will show
up; if we're not, it could be six. The next FOTD will be posted
in 24 hours, possibly as little as 14 hours. Until whenever,
take care, and what will be the next big breakthrough?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Mount_Mountain { ; time=0:12:49.73-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=t
center-mag=-0.0853596/0.776714/7.814454/1/-142.5/0
params=1.1/0/11/525 float=y maxiter=32767
inside=253 logmap=63 periodicity=6
colors=000QGaQH`QH_PIYPJXOKWOLVOMTNNSKORHOQHPOHQNG\
RMGSLGYJFUIFVHFVGGWHGRIHRIHRJIRKIRKJWLJWLJWMKWNKWN\
LWOLRPMRPMRQNRQNRRNRSORSORTPRTPRUQRVQRVRRWRRXRRXSR\
YNRYORZOR_PR_PR`OT_PS`PR`QQaQQaQPbRObRNcRNcSMdSLdN\
_eOZeOYfOXfPXgPWgPVgQUhQUhQTiRSiRSjRRjSQkSPkSPlbOl\
bNmbNmcMncLncKndKodJodIpeHpeHqeGqfFrfFrfEsgDsgCrgC\
mhBhhAccFZZKUUPTPUKKZFFcEAcE5cE3bE3aE4`E4`E4dE4cD4\
bD4bD5aD5`D5`D5_D5ZD5YD5YC6XC6WC6VC6VC6UC6TC7SC7SC\
7RB7QB7QB7PB7OB8NB8NB8MB8LB8KA8KA9KA9KAUcAUKAmKAUc\
AmKAUK9Uc9mK9UK8UK8mK8Uc8UK7mK7UK7Uc6zE6cD6zD6cD5c\
D5zD5cD5cD4zD4cD4cD3zD3cD3cC3zC2cC2cC2cC1cC1cC1cC1\
cC0cC0cC0cC0cJ4cP7IWBMaEPhIQgHRgHSfHSfHTeGUeGVdGVd\
GWdGXcFYcFYbFZbF_aE_aE``Ea`Eb`Em_Dm_DmZDmZDmYCmYCm\
YCmXCmXCmWBmWBmVBmVBmUAmUAmUAmmAmmAmm9mm9mmzmmzmmz\
mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\
zmmzmmzmmzmmzmmz00ammzmmz }
frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z|<a }
END PARAMETER FILE=========================================
FOTD -- November 24, 2010 (Rating 5)
Fractal visionaries and enthusiasts:
As I said in yesterday's FOTD, I have grown bored with the odd
slices of the Julibrot, and have decided to return to the old
familiar routine images a week early.
Today's image lies in a remote valley of the strange parent
fractal that results when the formula Z^sqrt(2)+C is iterated
41.3 levels up the complex logarithmic ladded with no function
applied.
The minibrot at the center is a square-root-of-2 thing. With
exponents of Z in this range, parent fractals and their mini-
brots can take any shape whatever, which is not surprising,
since the complex logarithm is multi-valued.
The name "Busy-body Blueness" is one of the most unjustified I
can remember. Very few blue tints are in the image, which is
more of a sickly olive-green and orange than anything else. I
have no idea what the 'busybody' is supposed to refer to.
The rating of a 5 might have been higher if I had put a bit more
effort into the coloring.
The calculation time of 5-1/4 minutes is asking a bit much from
the casual viewer to see a 5-rated image, but those who decline
to view it will never know what they have missed.
Running the included parameter file may not be necessary. The
finished image is likely posted on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Clouds prevailed all day Tuesday here at Fractal Central, but
they broke in the west just before sunset, leading to a spectac-
ular light show. The temperature reached a pleasant 57F 14C.
The fractal cats took things easy until late afternoon, when
they began agitating for food.
My day was a very boring average, but then who needs excitement
all the time. The next FOTD will be posted in 24 hours. Until
then, take care, and the fractals will keep coming until the
supply is exhausted.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Busy-body_Blueness { ; time=0:05:14.45-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=+0.09186130753/+1.498879230002/2387775/\
1/110/0 params=1.4142/0/41.3/0 float=y maxiter=8400
inside=0 logmap=362 periodicity=6
colors=000qPLqPLqPMqPNqPOqPPqPPpPQpPRpPSpPSpPTpPUp\
PVpPVoQWoRXoSYoTYoUZoV_oW`oXboY`mZ_k_Yh`XfaWdbUacT\
_dRYeQVfPTfNReMOdKMcJJdJKcILcHLbGMbFMaFN`ENZDOYCOX\
CPdBPcAQa9Q`9RZ8RY7vW6vV6vU5vS4vR3vP3vO2sM1pL0mK0j\
M2gN4dO6aP8ZQAXRCYSEYTGYUHYVJYWLYYNYZPZ_RZ`TZaVZbW\
ZcYZd__ea_fc_ge_ig_ji_kj_ll`mn`np`or`pt`qv`rx`sy_q\
wZpvZouYnsYmrXlqXkoWinVhmVgkUfjUeiTdgTcfSaeR`dR_bQ\
ZaQY`PXZPWYOUXNTVNSUMRTMQRLPQLOPKMOJKMJILIGKIEIHCH\
HBGG9EF8DF7CE6AE59D48D37E58F78FA9GC9HE9HHAIIAIJAJL\
BKMBKNBLPCLQCMRCNTDNUDOVDOXEPYEQZEQ`FRaFRbFQ`KQ_UP\
ZcPXjOWcOVUNUKNSCMRCMQCLOCLLBKJBKHBJFBJDAICAIBAIBA\
HD9GF8GI8FK7FL6EO6EQ5DS4CV4CW3BY2Be2Af1Ag1lh2li3lj\
4lk5ll6lm7ln8lo9qpAqqBqrCqsDqtEquFqvGqwHqxIqyJqzKq\
zLqzMvzNvzOvzPvzQvzRvzSvzTvzUzzVzzWzzXzzYzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z|<a }
END PARAMETER FILE=========================================
