FOTD -- November 13, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
As the name of today's image -- "Juliptic Minibrot" -- implies,
today's image lies in an orientation half way between the
Elliptic and Julia directions. The center of the slice is the
origin of the Julibrot.
The image lies just east of a larger minibrot on a kind of main
spike of the parent fractal, which is shaped the same as the
minibrot in today's image.
Quite a bit of trickery was necessary to bring today's image to
a reasonable proportion. It was necessary to expand the X-axis
direction to nearly ten-thousand times its normal size. The
unexpanded view of the same area is only a series of vertical
stripes.
A minor coloring trick -- rendering the scene with the outside
set to 'tdis' -- brought just enough extra oomph to the image to
qualify it as FOTD for the day.
The rating of a 6 is based more on mathematical curiosity than
artistic value.
The calculation time of 5-1/2 minutes is slow for an image that
rates only a 6. I recommend viewing the image in finished form
on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Hopefully Paul is well enough to bring the site is up to date.
The last time I checked, the last posted FOTD was November 2.
Thursday began with fog here at Fractal Central, but by 9am the
sun broke through, and for the rest of the day total sun
prevailed, with a temperature of 57F 14C. The fractal cats made
the most of the sun, which at its low angle, comes in their
window quite strongly. My day was occupied with wrapping up the
week's work. The next FOTD is due in 24 hours, but if it is
late, an antiquing trip most likely arose on Saturday. Until
whenever, take care, and be ready to sacrifice.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Juliptic_Minibrot { ; time=0:05:31.15-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=-2.474863995\
1095/0/915153/9451 params=90/0/45/0/0/0/0/0 float=y
symmetry=xaxis maxiter=15000 inside=0 outside=tdis
colors=000zm0KgGIkIHnKCjU7fc3cl9`hEZeJWaOUZURVZPSc\
MOhKLlGWpCet8ow4yU6STAVSEXRH_RLaQPdPSfOWiOZk97_ois\
llbjoMhr6bhFY_OTRXOIeJ9mavGUDGVHEWLCXPAYT9ZX7_`5`d\
3`g2RbIHZX7IY6DZ6DUAAUA7UA5UA6UA6UA6NACVAIbFNjKTrH\
YzKUtNQnQNiTJcWFYZCTa8Nd5IeKTzYcelnzzyzrqzzinbapWU\
sOMvGEx97r8Cm7Gh6Lc6PZ5UU4YP4aM6KJ8`G9KDB`ADK8E`9G\
K9HcAJKAKfBLKBNiCOjCPkFUgHYdKa`MeYOiURmRTqNVuKXzQz\
rWZza`pgazmznsazpaln`zk`ji_zfzhdZgazg_YfXYeVXdSXcQ\
WbNWaLWaJx`VyYVx_Qx`MxbIwcEweAwf6wg2ue5tc7sa9q`CpZ\
EoXGmVJlULkSNiQQhOSgNU_TWTYXMcZEh_7na0sbLpaemazkav\
icsgepffldhicifakb`l_ZnXYoa_nf`mkalpbkucjl`ccZYWWR\
NULERE6P88OD9NHBNMCMQDLUFLZGKbHKfwmNsnPpoRmpSjqUgr\
WcrX`sZYt_VuaSvcOvdLwfIxhFyiCzk9zlBvjDshEofGldIhbJ\
e`HbZF`YEYXCWWBTV9RU7PS6MR4KQ3HP1FO0DN2GQ4IT6LW8NZ\
APaCSdEUfGXiIZlK`oMcrOeuPgwQfuResSdrTcpUbnVamW`kX`\
jQZlKXnDVp7Tr1Rt7SsQYAO`C }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
A presentation of blue swirls. Ready made at http://maxitersfractalfollies.blogspot.com
Blue Swirls { ; fract504.gif noodle-ish
; blank
; calctime 0:04:06.84
; created Nov 11, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=conic.frm formulaname=km_08
center-mag=-0.894769/0.249144/2.693612/1/180
params=-0.2698141422772912/-0.1384014404736473/-0.195287942136906/0.3802\
30109561449/0.1877803888058107/0.9158909878841517/-0.9793694875942259/0.\
6154667806024354 float=y maxiter=1500 inside=0 outside=atan
decomp=128
colors=atubuvcwwdxxfzzfzzeyydyydxxcwxbvwavwauv`tv_tuZsuYrtYqtXqsWpsVorVo\
rUnqTmpSlpRloRkoQjnPjnOimOhmNglMglLfkLekKejJdjIciHbhHbhGagF`gE`fE_fDZeCY\
eBYdAXdAWc9Wc8Vb7Ub7Ta6Ta5S`4R_3Q_2PZ2PZ1OY0NX1NX2OY3PY4QZ5R_6R_7S`8Ta9U\
aAVbCWcDXcEYdFZeG_eH_fI`gJagKbhLciMdiNejOfkPgkQhlRhmSimTjnUkoVloXmpYnqZo\
q_pr`qsaqsbrtcsudtueuvfvwgwxhxxiyykzzjyyixyhwxgwxfvweuvdtvcsubrtart`qs_p\
sZorYnqXmqWmpVloUkoTjnSinRhmQhlPglOfkNekMdjLciKciJbhIagH`gG_fFZfEZeDYdCX\
dBWcAVb9Ub8Ua7Ta6S`5R`4R_3QZ2PZ1OY0NX1NX2OY3PY4QZ5R_6S`7T`8Ua9VbAWcBXcCY\
dDZeE_fF`fGagHbhJciKdiLejMfkNglOhlPimQjnRkoSloTmpUnqVorWprXqsYrtZsu_tu`u\
vavwbwxcxxbwxavw`uvZtuYrtXqtWpsUorTnqSmpRkoPjnOimNhmMglKfkJdjIciHbhFagE`\
fD_fCYeAXd9Wc8Vb7Ta5S`4R_3QZ2PY0NX1OX2PY3QZ4RZ6S_7T`8Ua9VbAXbBYcDZdE_eF`\
fGafHbgIchKdiLejMfjNgkOhlPimRjnSlnTmoUnpVoqWprYqrZrs_st
}
frm:km_08 { ; Kerry Mitchell 11may98
; originally conic-near_jul16
; tweaked by rjr 2k04 to allow user to directly input
; julia parameters previously hardcoded to 0.2882,0.0106
cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1
a=real(p1), b=imag(p1), c=real(p2), d=imag(p2)
e=real(p3), f=imag(p3):
iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc)
conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f|
if (conic<minr)
minr=conic
end if
if ((|zc|>maxr)||(iter==maxit))
iter=-1
t=log(minr)
z=cos(t)+flip(sin(t))
end if
iter>0
}
Roger Alexander
FOTD -- November 11, 2010 (Rating 8)
Fractal visionaries and enthusiasts:
A busy day means a late FOTD. Wednesday was unusually busy here
at Fractal central, so the FOTD is late.
Today's image lies in the parent fractal of yesterday's image.
It is located in the Seahorse Valley of a distorted minibrot on
the main stem of the parent, very near the point where the stem
joins the main body of the Julibrot fractal.
I named the image "Not a Julia Thing". On the surface it
resembles an everyday Julia set, but it actually lies in an
orientation rotated halfway toward the Mandelbrot direction,
making it something for sure, but not a pure Julia set.
The rating of an 8 includes a full point for the extra effort I
put into coloring the image. The coloring creates the better
part of the overall effect.
The calculation time of over 1-1/2 hours that is listed in the
parameter file is some kind of timing bug that sometimes appears
in the fractal computer after I run the ancient 'WordPerfect 5.1
for DOS' program, which I still use after all these years. The
actual calculation time is around 2-1/2 minutes. It's too bad
the bug doesn't make the fractals calculate as fast as it makes
the clock run. (While the bug was in effect, the calculation
time for an hour-long fractal was listed as 'a very long time'!)
The finished image may be seen by running the included *2-1/2*
minute parameter file or by viewing it on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Total sun and an unexpectedly warm temperature of 61F 16C kept
nearly everyone happy here at Fractal Central on Wednesday. The
fractal cats actually had a bit too much sun in the afternoon,
and retired to the bookshelves in the hallway.
My day was quite busy, yet satisfactory, which is all I could
hope for. The next FOTD will probably be posted in 12 hours.
Until then, take care, and when all those predicted technolog-
ical wonders finally arrive, will they be for everyone, or only
for the wealthy?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Not_a_Julia_Thing { ; time=1:31:02.06-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=-0.944342858\
62/+0.000172719906/4812174/1/-40/0 params=45/0/-45\
/0/-0.75/0/0/0 float=y maxiter=5000
inside=0 logmap=614 periodicity=6
colors=00000B00D00F00I00K00N00P00S00V00Y00_01b02d0\
3f04h05j06l07n08o09p0Aq0Br0Cs0Ds0Es0Fs0Gs0Hs0Is0Js\
0Ks0Js0Ks0Ls0Ls1Ms2Ns3Ns4Os6Pr7Pq8Qp9RoARnBSmCTlDT\
lASm8TnAUnCVoEWpGXpIXqKXrMXrOYsQYsSYsUYsWZsYZs_Zsa\
_sc_se_sg_sh_si_sj_sk_sl_sm`sm`sm`sm`sm`sm`sm`smas\
masnasobspfsqfsrgssgssestfstgsuhsujsvksvlswmswnswo\
swpswqsvrsurstrssrsqrsqrsqssqtsqutsvtuwuwxusxvszws\
zxrzyrzzrzzrzzqzzqzzqzzqzzpzzpzzpzzpzzpzzpzzpzzpzz\
pzzmzzozznzzmzzmzzmzzmxznxzmxzlxzkxzkxzkxzkxzkxzkx\
zkxzkxzjxzjxzjvzivzhuzgvzftzetzdrzcqzarz_qzYpzWqzU\
qzQpzMpzIpzGqzGrzGsyFtxEvw8uv2su0rt0ms0is0es0as0Zn\
0Wi0Td0Q_0NV0KQ0HL1EI1CI0AI08L09P0CT0EX0I_0Lc0Og0R\
m0To0Vq0Xs0Ys2Ys3Zs5Zs6Zs8ZsAZsBZsD`sFbsGdsIfsJhsN\
jsRlsWns`psdpshwshwshwshwshwsdrs`tsWvsRwsHlsCbs7Ss\
2Is0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0B\
s0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
FOTD -- November 10, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Like all images in the month of November, today's image lies in
an unfamiliar slice of the Z^2+C Julibrot. I'll not try to
describe the location or orientation of the parent-fractal
slice, other than reporting that it is centered on Seahorse
Valley and is double-rotated halfway between the Mandelbrot and
Julia orientations. This is little help, since in the 4-D
Julibrot there are countless orientations halfway between the M
and J directions. Today's scene is located on the rudimentary
main stem of the parent slice.
I named the image "The Mystical Donut". I know it's a rather
silly name. There is little of a mystical nature in a donut.
But I can't help it if I saw a donut in the image.
Most of the image's detail was created by rendering it with the
outside set to 'real'. The 'imag' and 'summ' options work
almost as well.
The rating of a 7 makes the image worth the minute required to
run the parameter file.
Those with over-qualified machines can hopefully find the eye-
ball-ready image posted to the FOTD web site at:
<http://www.Nahee.com/FOTD/>
A mixture of sun and clouds prevailed here at Fractal Central on
Tuesday, with the clouds predominating. The temperature of 55F
13C was just a bit too chilly for maximum comfort, though it was
about normal for early November. The fractal cats enjoyed the
sun when it appeared and sought comfort by the heat when it went
behind the clouds.
My day was average. Isn't that boring? The next FOTD will be
posted in 24 hours. Until then, take care, and do we exist even
when we are unconscious?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
The_Mystical_Donut { ; time=0:01:03.50-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=-1.41420407/\
0/724383.1/1.5564/-90/0 params=45/0/-45/0/-0.75/0\
/0/0 float=y maxiter=1400 inside=0 outside=real
colors=000JffIeeIddIccIbbIbaIb`Ib_IbZIbYIbXIbWIbVI\
bUKaTLaSNaROaQQaPSaOTaNVcMXeLYgK_iK`kKdmKhoKmqKrsK\
vs2zz2zzzzzzzzzzzzvuzrw2my2hz2ZoCUeMPVWKLfGApCAzB8\
vB6tB4rB3oB3mA4kA4iA5gA6eA6dA7c97b98a98`99_9AZ9AY8\
BX8BW8CV8CU8DT8DS7ER7EQ7FP7FO7FN7GM7GL7GN7HP7HS7IU\
7IW6IZ6J`6Jb6Je6Kg6Ki6Ll6Ln6Lp6Ms6Mu6Mw8Nv9OuAPtBP\
sCQrDRqERpGSoHTnITmJUmKVlLVkMWjOXiPXhQYgRZfSZeT_dU\
`cV`cSZdQYeOXeMWfJVgHUgFThDRiBQi8Pj6Ok4Nk2Ml0Ll2Nh\
3Od4Pa5QY6RU7SR8TN9UJAVGBWCCX8DY5BaDAeL9iT8l`AmaBm\
bDmcEmdGmeHnfJngKnhMniNnjOnkQolRomTonUooWopXpqZpr_\
psaptbpucpuensflrgkqhipigojfnldlmcknajo_ipZhqXgrWf\
n_djbcffabi`Zm_VpYRtXOwWNtVMqVLoVKlVJjUIgUHeUGbUF_\
UEYTDVTCTTBQTAOTCPUDQUERUFSUGTUHUVIVVJWVKXVLYVNZWO\
_WP`WQaWRbWScXTdXUeXVfXWgXVeUVcSVbQV`OV_MVYKUXIUVG\
UUEUSCURAUP8UO6SSDQWKP_QNcXMgbKkiJnoKnpKnpKnpKnpKn\
oKnnKmmKllKkkKjjKiiJhhJgg }
frm:SliceJulibrot2 {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
Today's blog post of Fractint compatible gifs and anti-aliased jpgs is of two versions of
the field4_jul formula by Kerry Mitchell. They are identical except for the imaginary P2
values. I calculated with values of 0 and 12. Available at http://maxitersfractalfollies.blogspot.com
I've posted only one version of the par file, just vary imag(P2) if regenerating.
Field Line Variations { ; fract506.gif
; blank
; calctime 0:03:55.63
; created Nov 08, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=*.frm formulaname=field4_jul
center-mag=0.048197/0.607759/3.404629 params=0.375/0.375/1000000/0
float=y maxiter=1500 inside=0 decomp=256 periodicity=0
colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\
J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\
`DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\
mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\
vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\
zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\
zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\
uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\
kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\
ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\
G48F48E47D37C36B36A35A259248247236135124124113012001000
}
frm:field4_jul { ; Kerry Mitchell 20jan98
;
; Colors Julia sets by nearest approach to
; period 4 field lines
;
; use decomp=256
; p1 = Julia parameter
; real(p2) = bailout (try 1e12)
; imag(p2) = number of field line to use: 0 - 15
; 4 iterations per pixel
; variable zc used for calculation, z for coloring
;
zc=pixel, c=p1, maxr=real(p2), minr=maxr, iter=1
fieldangle=tan(imag(p2)*2*pi/15):
;
; iteration
; compare tangent of polar angle with desired
; field line angle, update minimum if needed
;
iter=iter+4, zc=sqr(zc)+c, zc=sqr(zc)+c, zc=sqr(zc)+c
zc=sqr(zc)+c, rzc=|zc|, tanangle=imag(zc)/real(zc),
r=cabs(fieldangle-tanangle)
if (r<minr)
minr=r
end if
;
; bailout
; set "iteration done" flag (iter=-1)
; use log of minimum difference of angles as
; decomposition angle
;
if ((rzc>maxr)||(iter>=maxit))
iter=-1
angle=log(minr)
z=cos(angle)+flip(sin(angle))
end if
iter>0
}
Roger Alexander
FOTD -- November 09, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is (no guarantee) the last of the series of near-
Julia Mandelbrot valley images. This one shows the valley of
the north bud of the large minibrot on the west branch of the
filament that extends from the north bud of the Mandelbrot set.
The effect is much the same as the previous images, though there
is more decoration around the almost-Julia set. The name "Hour-
glass Spirals" refers to the hourglass-like shape of the two
spirals on either side of the center.
It is tempting to think of these fractal spirals as 3-D things
such as short curved lengths of string. But they are actually
2-D slices of 3-D spaces that curve and twist in 4-D space. As
with all 4-D stuff, the entirety of the spirals is impossible to
visualize. As mere humans, our consciousness is limited to the
3-D experience.
I decided to give today's image, which is likely the last of the
series, a rating of a 7. We have been mired in this series
longer than I had intended, and there are many unusual slices of
the Julibrot that we have not yet checked. Tomorrow's image
will begin the exploration of these.
Today's image calculates in under 7 minutes, not fireball fast,
but certainly faster than some FOTD's, which have taken days to
complete.
The last I heard, Paul was still in the hospital, recovering
from an infection. He has enough access to the FOTD web site to
post the FOTD discussions. But since he is using a new-fangled
laptop machine running Vista, which panics as the sight of the
Fractint program, he cannot run the parameter files. I am send-
ing the finished GIF images to him while he is in the hospital,
from where he can post them to the FOTD web site. Hopefully,
the web site will be up to date shortly. As always, the site
may be accessed at:
<http://www.Nahee.com/FOTD/>
A few too many clouds and a bit too little sunshine here at
Fractal central on Monday kept the fractal cats from reaching
maximum contentment. The temperature of 54F 12C was just about
normal. My day was normal also.
The next FOTD will be posted in 24 hours. Until then, take
care, and I hear that within 25 years everyone will have their
own private autogyro for their daily commute.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Hourglass_Spirals { ; time=0:06:51.18-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1 center-mag=0/0\
/11.7/1/87/0 params=89.9/0/89.9/52.5/-0.15436/\
1.0371225/0/0 float=y maxiter=40000 inside=0
logmap=8 periodicity=6
colors=000CKVDLUEMSFNWGOTHPRIQOJRMJSJKTIMUJNVIOWIQ\
XHTYGVZGY`F_aFabEdcDfeDifCkgCnhBpjAskAul9wm9zlCzlE\
zlHzlJxlMvlOtlRtlTslWslYsl`rlbrlerlgqljqllqlnokmnj\
lmikkijjhiifhgdhfegedfcbecadcaccaccabcbacc`cc_ccZc\
cZccYccXccWccVccUcbUcaYc`acZecXicWmcVqcUpcUpcUpdUp\
dUpdUpeUpeUoeUofUofUofUogUogUogUnhUnhUnhUniUniUnjU\
nkUmlUlmUkmUjmUimUhmUhmUgmUfmUemUfmUgmUhmUhmUimUjm\
UjmUkmUlmUlmUmmUnmUnmUomUpmUpmUpmUqmUrmUsmUtmUumUv\
mUwmUxmUymUxmUxmUxmTxmSxmRwmQwmPwmOwmNwmMwmLvmKvmJ\
vmIvmHvmGumFumEumDumCumBuiEteHtaKsYNsUQrSRrQSrOTsM\
UsKUsIVsGVsEWtCWtAXt8Xt6Yt4Zu2_u0`u0bz0dz0ez0ez0fz\
0fz0gz0hz0hz0hz0iz1jz3jz4kz5kz7kz8qzArzBrzCszEszFs\
zHuzIuzKuzLuzMuzOuzPuzRuzSuzSuzUzzVzzWzzXzzYzzZzz`\
zzazzbzzczzdzzezzgzzhzzizzizzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
FOTD -- November 08, 2010 (No Rating)
Fractal visionaries and enthusiasts:
Today's image is what happened when I tried the almost-Julia-
valley trick on the valley leading to the large sub-bud on the
northwest shore line of the large period-2 bud of the Mandelbrot
set.
Like the recent images, there are some similarities and some
differences. The greatest difference in today's image is the
fact that it is only the central part of the entire parent
almost-Julia set. I have cropped off a good part of the out-
lying areas, but the part that remains is interesting enough.
We have the same spirals and the same grossly enlarged view of
the Mandelbrot aspect of the valley. Once again I used mostly
the same color palette, though in today's image I cut the values
and intensity of the stronger hues.
I could hardly give just another valley scene a proper rating,
though I did name it "Be Forever Fractal", a name that sounds a
bit more meaningful than it actually is.
The calculation time of only 3 minutes is blessedly brief. (I
gave it the blessing myself.) I haven't heard how Paul at the
FOTD web site is coming, but the last I heard he was recovering,
so it might be worth a look to see if the FOTD web site at:
<http://www.Nahee.com/FOTD/>
is up to date yet.
FL and I managed the shift from daylight time to standard in
fine shape here at Fractal central on Sunday. We simply arose
an hour earlier. The cats never noticed the change, except in
the evening, when they had to wait an hour longer for their
treats.
A mixture of sun and clouds hung above Fractal Central all day.
The fractal cats enjoyed the sun while it was out and the house
heat when the sun failed them. The temperature of 45F +7C was
chilly for both man and cat.
The next FOTD will be posted in 24 hours. There is no escaping
the delay. Until then, take care, and resistance is futile.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Be_Forever_Fractal { ; time=0:03:07.19-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1 periodicity=6
center-mag=0/0/2.16/1/47.5/0 float=y maxiter=42000
params=88.7/0/88.7/77.5/-1.12542/0.21722/0/0
inside=0 logmap=yes
colors=00086a97bA8cB9dCAeDBfECgFDhGEiHFjIGkJHlKImL\
JnMKoNMnOOmPQlQSkRUjSVgTWdUXaSY_QZXOZUMYSKXQIWOGVN\
EULCTJASH8RE6QB4P95OA5NA5MA5LA5KB5KB5KB5KB6KC6KC6K\
C6KC6KD6KD6KD6KD8KC9KBALBBNADQ9ES9FU8GW8IZ7J`6Kb6L\
d5Mf5Qb9T_DUXHUULUQOUNSUKWUH_UEbUFaUF`UF_UG_UGZUGY\
UGXUHXUHWUHVUHVULWUOWURWUVXUYXU`XUaTUaPSbMQbIOcFQc\
BSd8Ud4Wd0YdA_dKaeUceZceccfccf_ceZcdYccX`cWZcVWcUT\
cTQcRNcQLcPIcOFcNCcM9cL7cKEcJLcJScIZcIccMMc7Oc8Mc7\
Lc7Mc7Nc7O`7PY6QV6SU6UU6WU6YU6_U5aU5cU5cU5cU5cU5cU\
7cU8cU9cUAcUCcUDZUEUUFPUHKUIFUJAUK5UM3UN3UO3UP3UR3\
US4VT4WW4YZ4Zc4`h4am4cq4ev4fw5ix5jy5lz5nz5oz5oz5pz\
5pz5qz3rz5rz6rz8sz9tzBtzCuzDuzFuzGvzIwzJwzKxzMxzNx\
zPzzQzzSzzTzzUzzWzzXzzZzz_zz_zzazzbzzczzdzzezzfzzh\
zzizzjzzkzzlzzmzzozzpzzqzzqzzqzzqzzqzzrzzrzzrzzrzz\
rzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrz\
zrzzrzzrzzrzzrzzrzzrzzrzz }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
