FOTD -- November 07, 2010 (No Rating)
Fractal visionaries and enthusiasts:
The lateness of today's image is due to a not-so-surprise
antiquing expedition that arose not-so-unexpectedly on Saturday.
But better late than never.
Today's FOTD is the parent fractal of yesterday's 'Almighty
Spiral' fractal. The actual spiral that filled yesterday's
image lies humbly at the right edge of today's scene.
Many other spirals fill the upper half of the image, which lies
on the bud side of the Mandelbrot valley that is visible as the
two brilliant wedges jutting across the center of the outer
shape. The lower half of the image, which is the main-bay side,
has no spirals at all.
Today's image is not a Julia set, but it comes very close. It
is double-rotated 0.04 and 0.04 degrees from the actual Julia
orientation. (Double rotation is a mathematical abstraction
most difficult to comprehend. Nothing at all like it exists in
three-dimensional space.) But the orientation of today's image
produces many Julia characteristics and also shows the position
of the hairline spirals in relation to the Mandelbrot aspect of
the area.
With today's image being a near-repeat of yesterday's, I could
give it no rating. The name "Home of the Spiral" needs no expla-
nation however.
The calculation time of almost 10 minutes will need to be
endured in nail-biting impatience. I hear that Paul Lee has
been in the hospital for over a week, and has been unable to
update the FOTD web site. Fortunately, he appears to be on the
road to recovery.
But a trip to the FOTD web site that he has maintained for over
13 years and that holds the past FOTD images is always a lot of
fun. The web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Heavy scudding clouds, blustery north winds and a temperature of
43F +6C made Saturday quite brisk here at Fractal Central. The
fractal cats had enough heat inside that they never noticed the
outside chill.
When the antiquing was over and done, my day was reasonably
settled. The next FOTD will be posted in 24 hours. Until then,
take care, and the answer may lie where least expected.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Home_of_the_Spiral { ; time=0:09:52.49-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1
center-mag=0/0/0.8503401/1/126/0 periodicity=6
params=89.96/0/89.96/0/0.3272613/0.0561252/0/0
float=y maxiter=150000 inside=0 logmap=yes
colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\
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wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\
rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\
zrwzrwzrwzrwzrwzrwzrwzrwz }
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=========================================
Today's post is a spiral, perhaps not as impressive as Jim Muth's FOTD 06-11-10
but incontestably a spiral. Ready made at http://maxitersfractalfollies.blogspot.com
Yet Another Spiral { ; fract502.gif
; blank
; calctime 0:10:07.09
; created Nov 06, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=kerrym.frm formulaname=km_04
center-mag=0.167019/0.535127/24.2564
params=-0.5/-0.5/-0.6354869228186896/-0.3533127842036195/-0.173558763389\
996/-0.1402325510422071/0.08810693685720389/-0.7196569719534898
initorbit=0.3/-0.6 float=y maxiter=1500 inside=0 decomp=256
periodicity=0
colors=DHVCGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\
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nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW
}
frm:km_04{; Kerry Mitchell 26aug98
; tweaked by rjr so user can input julia parameters
; See the end of the formula general_man-2circ for
; Kerry Mitchell's explanation of the "2 circles
; coloring method".
;originally general_jul_test
; "2 general circles" coloring method for Julia sets
; c = Julia parameter, hardcoded originally to (0.65,0.33)
; p1 = x-circle center
; p2 = y-circle center
; real(p3) = x-circle radius
; imag(p3) = y-circle radius
; bailout hardcoded to 10^12
; use "decomp=256" coloring
;
zc=pixel, c=p4, bailout=1e12, iter=1, rmin=1e12
cenx=p1, radx=real(p3), rad2x=radx*radx
ceny=p2, rady=imag(p3), rad2y=rady*rady:
iter=iter+1, zc=sqr(zc)+c
tempx=|zc-cenx|-rad2x
tempy=|zc-ceny|-rad2y
temp=tempx+flip(tempy), r=|temp|
IF (r<rmin)
rmin=r, z=temp
ENDIF
IF ((|zc|>bailout)||(iter==maxit))
iter=-1
ENDIF
iter>0
;SOURCE: 98msg.frm
}
Roger Alexander
FOTD -- November 06, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
Usually, I put little effort into fractal spirals. They're very
easy to find and nearly everyone does them. But the spiral in
today's image is so unusual that I had to make it a Fractal of
the Day.
I found the spiral when I tried to extend the trick of the two
most recent FOTD's to the valley of the period-10 bud on the
northeast shore line of the Mandelbrot set. The trick worked as
I thought, producing the anticipated image, but I never expected
the image to be filled with such hairline-thin spirals.
Today's scene is a blow-up of a small part of the full image,
which in itself is quite interesting. (The full image will be
the FOTD for tomorrow, November 07.)
Actually, images with very fine details such as today's and
tomorrow's are improved by anti-aliasing, which helps eliminate
the awkward breaks in the finer parts. Because of the fine
detail in today's image, I recommend calculating it at the
highest resolution available.
The name "Almighty Spiral" is overblown. The spiral is not all
that great when compared to some that have been found by others,
though it is probably the best I have found.
If spirals were not so commonplace, I might have rated the image
higher. As it is, a rating of a humdrum 6 will have to do.
The calculation time of 11 minutes is for a resolution of
640x480. It will be far longer if the image is rendered at a
higher resolution than this. But for the true fractal-spiral
fan, the result will be worth the wait.
The finished image is posted on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Sprinkles of rain fell during the morning Friday here at Fractal
Central. A few breaks of sun appeared during the afternoon, but
not enough to lure the fractal cats to their shelf by the south-
west window. The temperature of 52F 11C was about normal for
early November.
The next FOTD will be posted in 24 hours. Only a surprise
antiquing trip could delay it. Until next time, take care, and
expect the unexpected.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Almighty_Spiral { ; time=0:11:12.40-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=t periodicity=6
center-mag=-0.448511/-0.894674/9.159484/1/114/0
params=89.96/0/89.96/0/0.3272613/0.0561252/0/0
float=y maxiter=15000 inside=0 logmap=-3
colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
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rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\
zrwzrwzrwzrwzrwzrwzrwzrwz }
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=========================================
Today's post is another formula by Kerry Mitchell based on the Julia iteration loop.
Gif and jpg version available at http://maxitersfractalfollies.blogspot.com
Threaded Julia { ; fract499.gif another Julia iteration loop fractal
; blank
; calctime 0:05:22.08
; created Nov 04, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=kerrym.frm formulaname=km_08
center-mag=-0.730914/0.135225/2.109705
params=0.5243385113071077/0.07968382824182867/-0.8776207770012513/-0.809\
0762047181616/-0.5746330149235511/0.3112582781456953/-0.8414868617816705\
/0.2847071749015778 float=y maxiter=1500 inside=0 decomp=256
periodicity=0
colors=000734633523422312211101000000100200311411512612723823924A34B35B3\
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}
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 05, 2010 (No Rating)
Fractal visionaries and enthusiasts:
I rather enjoyed the half-and-half view of Seahorse Valley that
I posted as the FOTD for yesterday. Today I decided to take it
one step further and see what would happen if I calculated the
same type of view of North Valley. The result is today's image.
The image closely resembles yesterday's, with the outer shape
being the familiar Julia set of the area, with the bloated
Mandelbrot-valley aspect filling the inside.
At first glance, today's image appears to have origin symmetry.
A second glance however reveals that it has no symmetry.
An even greater change is in the periodicity. In yesterday's
image the blunt spirals had two arms; in today's image there
are three arms in each spiral.
I re-used the same color palette to bring out the similarities
in the images. But this makes today's image too much of a
repeat for an honest rating. I let it go with no rating.
The name "Order-Three Nonsense" refers to the periodicity of the
area of the Julibrot pictured in the image.
The calculation time of 46 seconds is just about what the image
is worth.
The most convenient way to view the Julia-Mandelbrot nonsense is
to view the finished image on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Heavy clouds, steady rain, and a temperature of 46F +8C spoiled
outdoor plans here at Fractal Central on Thursday. Luckily,
with no outdoor plans, the fractal cats were satisfied indoors,
lying by the heat.
My day was tranquil enough, which means enough work to keep my
thoughts reasonably free of politics, philosophy and personal
opinions in general.
Now that gardening season has ended, FL found herself with more
spare time than she knew what to do with, but a latin soap-opera
soon filled the empty time. (I wish I understood Spanish.)
The next FOTD, even higher-order nonsense, will be posted in 24
hours. Until then, take care, and will there ever come a day
when someone discovers the last fractal?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
OrderThreeNonsense { ; time=0:00:46.52-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1 symmetry=none
center-mag=-0.0201592/-0.0270368/0.9861933/1/58.5/0
params=87/0/87/58.7/-0.125/0.66/0/0 float=y
maxiter=2700 inside=0 logmap=yes periodicity=6
colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
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rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\
zrwzrwzrwzrwzrwzrwzrwzrwz }
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 fractal is the Nov. 2 formula with a new map and different parameters.
And at good ole http://maxitersfractalfollies.blogspot.com is yesterday's post re-sampled.
Yesterday's Post { ; fract498.gif
; blank
; calctime 0:13:29.11
; created Nov 03, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=kerrym.frm formulaname=km_10
center-mag=-0.63921378791777690/+0.42946123624707840/231.2811
params=-0.2080599383526109/1.29938962981048/-0.510940885647145/1.6808160\
64943388/0.2298806726279488/0.8896145512253182/-0.749626148258919/0.4
float=y maxiter=256 inside=0 outside=atan decomp=256 periodicity=0
cyclerange=0/255
colors=sz8sz8rz8rz8qz8py8py8oy8ny8nx8mx8mx8lx8kx7kw7jw7iw7iw7hv7gv7gv7fv\
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}
frm:km_10 { ; Kerry Mitchell 11may98
; originally conic-near_juli
; tweaked so user can directly input
; julia parameters (p4) originally hardcoded
; to 0,1
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 04, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image keeps us in Seahorse Valley. The image is
centered on the real(X) axis, just west of the valley itself.
The orientation of the slice is double rotated 5 and 5 degrees
from the actual Julia direction, which is close enough that the
outer shape of the Julia set of Seahorse Valley can clearly be
recognized.
The multi-colored arms thrusting into the outer Julia shape from
the sides are part of the Mandelbrot aspect of Seahorse Valley.
The open upper half of the fractal is part of the main period-2
Mandelbrot bud; the lower half is part of the main bay. The
colorful decorations are stuff that mostly lies in the perturbed
Mandelbrot sets.
Due to its fancy colors, I rated the image at a 7. The name
"Seahorse Games" was inspired by the colorful trimmings, such as
might be seen at a birthday party.
The calculation time of 14 seconds is a real bargain. The trip
to view the finished image on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
is equally brief, and more convenient than running the included
parameter file.
Wednesday began with fog here at Fractal Central, but by 10am
the fog cleared off, leading to a day with total sun, just what
the fractal cats needed to keep them happy. The temperature
rose from a sunrise 28F -2C until it reached a very typical 54F
12C in mid-afternoon.
My day was average, which is pleasant enough but leaves little
to discuss. FL had a similar day. The next FOTD, a trip to a
different part of the Julibrot, will be posted in 24 hours.
Until then, take care, and who's behind those wacko conspiracy
theories that the radiation emitted by cell phones is unsafe?
If the phones were unsafe, the phone companies would be warning
us, just like the tobacco companies warned us about the dangers
of smoking cigarettes.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Seahorse_Games { ; time=0:00:14.77-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1
center-mag=0/-0.025052/0.85034 params=85/0/85/90/\
-0.764/0/0/0 float=y maxiter=2500 inside=0
logmap=yes symmetry=yaxis periodicity=6
colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\
EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\
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TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\
5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\
zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\
wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\
rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\
zrwzrwzrwzrwzrwzrwzrwzrwz }
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=========================================
Today's post uses a formula using a Julia iteration loop producing
a spirals of threads design. Ready made at http://maxitersfractalfollies.blogspot.com
Spirals of Threads { ; fract492.gif
; blank
; calctime 0:06:08.77
; created Nov 02, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=kerrym.frm formulaname=km_10
center-mag=-0.550248/0.349382/6.884776
params=0.1263771477401044/0.1877803888058107/-0.8391064180425428/0.67070\
52827539903/0.1497543259987182/0.7999206518753624/-0.749626148258919/0.7\
06839197973571 float=y maxiter=1500 inside=0 decomp=256
periodicity=0
colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\
0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\
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3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\
1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\
0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\
0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\
0720720620620520520520420420420320320220220220120120010
}
frm: km_10 { ; Kerry Mitchell 11may98
; originally conic-near_juli
; tweaked so user can directly input
; julia parameters (p4) originally hardcoded
; to 0,1
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 03, 2010 (Rating 5)
Fractal visionaries and enthusiasts:
Today we enjoy another image from the Z^2+C Julibrot. The image
would normally have been discarded as soon as it appeared, but
November is the month of salvation for questionable images from
the Julibrot, so I decided to give today's image a chance to
show its stuff, or its lack of stuff.
The rating of a 5 is right in the middle of the rating scale,
which ranges from zero to ten. This leaves it to the individual
fractal fan to decide whether the 2-1/3 minute calculation time
would be worth the effort.
The scene lies in the Seahorse Valley complex of the Julibrot.
I have totally lost track of the location and orientation, and
of the amount of stretching and skewing I did on the scene, but
in the end, I was left with an image of a debris-filled hole
with a brilliant white stripe in the background, which on the
surface has no resemblance at all to anything normally connected
to Seahorse Valley.
The name "Valley of Surprise" has something to do with the
first impression of the image. If one looks closely enough,
however, they will see tiny hints of seahorse activity every-
where.
Finally, the 2-1/3 minute wait for the image to calculate may be
avoided by viewing the finished image on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
The total sun here at Fractal Central on Tuesday was spoiled by
a morning temperature of only 23F -5C and an afternoon high of
48F +9C. The fractal cats, who spent the day in the indoor
temperature of 68F 20C fully enjoyed the sun however. My day
was average. The next FOTD will be posted in 24 hours. Until
then, take care, stay alert, and prepare for a bombshell.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Valley_of_Surprise { ; time=0:02:19.88-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1
center-mag=-0.512268272656399/+0.0732312476231547/\
164.2885/5.3623/13.0817225561897121/65.54874842\
92186195 params=0/0/90/0/-0.76/0/0/0 float=y
maxiter=15000 inside=255 logmap=142 periodicity=6
colors=000dWteXsfXqgYohZmi_kj`ikaglbfmbencdodcpebq\
farg`sg`sf_sfZsfZsfYsfXrfXqfWpfWocXn`YmZZlX_kW`jUa\
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zczzczzezzdzzdzzczzczzbzzbzzazzazz`zz_zz_zzZzzZzzY\
zzYzzXzzXzzWzzWzzVzzVzzUzzUzzTzzTzzSzzRzzRzzQzzQzz\
PzzPzzOzzOzzNzzNzzMzzMzzLzzLzzKzzJzzJzzIzzIzzHzzHz\
zGzzGzzFzzFzzEzzEzzDzzuzz }
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=========================================
