Another quickie today, a Kerry Mitchell formula with gif and jpg
at the usual http://maxitersfractalfollies.blogspot.com.
Also I finally got around to re-sampling the Aug. 16 post.
fract424.gif { ; green tendrils
; blank
; calctime 0:12:31.88
; created Sep 17, 2010
; Fractint Version 2004 Patchlevel 9
reset=2004 type=formula formulafile=kerrym.frm
formulaname=field3_man passes=1
center-mag=-0.12869856067348150/+0.98735067767556690/237.828
params=10000000/7 float=y maxiter=1500 inside=0 decomp=256
periodicity=0
colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\
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}
frm:field3_man { ; Kerry Mitchell 20jan98
;
; Colors Mandelbrot set by nearest approach to
; period 3 field lines
;
; use decomp=256
; real(p1) = bailout (try 1e12)
; imag(p1) = number of field line to use:
; 0, 1, 2, 3, 4, 5, 6, 7
; 3 iterations per pixel
; variable zc used for calculation, z for coloring
;
zc=0, c=pixel, maxr=real(p1), minr=maxr, iter=1
fieldangle=tan(imag(p1)*2*pi/7):
;
; iteration
; compare tangent of polar angle with desired
; field line angle, update minimum if needed
;
iter=iter+3, 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 -- September 20, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
It's been a while since I posted an 'evaporated' image.....
Today's FOTD ends the drought. It's an evaporated image in a
valley of the indescribable parent fractal that results when
0.0003 part of Z(-11.3) is mixed with 0.3 part of Z(-1.3) and
(1/C) is added.
A fractal created with only negative powers of Z evaporates as
the bailout radius is increased, until finally, nothing but a
blank screen consisting of 'inside' stuff remains. The one-
googol bailout radius of today's fractal was more than enough to
entirely evaporate the original image, leaving only the 'inside'
stuff to fill the screen.
But the inside stuff was not quite dead, and the application of
the active 'bof61' inside fill has restored the scene to life.
Actually, the resurrected version is better than the original un-
evaporated one.
I named the image "Evaporated Special", which is a fair descrip-
tion. The rating of a 7 might have been a half-point higher if
I had devoted more time to the coloring.
The calculation time of over 10 minutes is slow enough to give
anticipation time to build. The anticipation stage may be by-
passed however by visiting the FOTD web site at:
<http://www.Nahee.com/FOTD/>
where the finished image is posted for immediate gratification.
Despite a few too many clouds, Sunday turned quite pleasant here
at Fractal Central. A light shower at sunset ended the day
refreshingly. The temperature of 81F 27C gave the local cookout
fans one final cook-out. The fractal cats went into stretch-out
mode when the inside temperature reached the limit of their
narrow comfort zone.
My day was fair enough. The next FOTD will be posted in 24
hours, give or take a few. Until then, take care, and wonder
what fractals are made of.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Evaporated_Special { ; time=0:10:23.79-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip
center-mag=+3.9140006688399/-0.3338075208496/\
1.012697e+009/1/-92.5/0 params=0.0003/-11.3/0.3/\
-1.3/0/1e+100/0/0 float=y maxiter=7500
inside=bof61 periodicity=6
colors=0006076987B97D98FATgLIUFIGlDGTu`OlXLdUJXQHO\
NEGJCnbgj`dgZbdY_aWYZUVWTTTRRQPONOMKMJHKHEJEBHC7bP\
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2sj3og3ld4ia4fZ5cW5`T6YR6VO7SL7PI8MF8JCofXjcUe`R`Y\
PWVMRSKMPHHMFCJC415536557 }
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=========================================
I was doing some deep zooming and I stumbled across this image. I liked the
dike like effect caused by the outside=tdis coloring method so I thought I
would post it. The letters at the end of the name are the date. Hopefully
there won't be any duplicate names that way.
There is an image at:
http://www.fracton.org/fmlposts/deep_jin.html
If you would like to draw it yourself. The par is:
Deep_JIN { ; Exported from Fracton.
; time= 8 min 0 sec at 640 x 480 with no aa
; on a Mac Pro 2 x 2.8 GHz Quad-Core Xeon
reset=2004 type=mandel passes=1 float=y
center-mag=-0.176859048709791371328447659161679877\
8e1/0.1606107349720067507002061168309015518e-2/3.6\
408889344e+22/1/-5/0
params=0/0/0/0/0/0/0/0/0/0 maxiter=80000 inside=0
outside=tdis bailout=9
colors=000BUIBSHAQG9OG9MF8KE7ID7GC6EB5CA5A9488X`XW\
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A6D96C96C86B76A66A669569468MzXLwWKuVKsUJqTIoSImRHk\
QGiPGgOFeOEcNEaMD_LDYKCWJ }
--
Mike Frazier
www.fracton.org
With Roger Alexander's permission I've created a high-res feed of the
parsets he's been posting for his "Max Iter's Fractal Follies" blog.
This is similar to the feed I've created for Jim Muth's Fractal of the
Day series.
Images: <http://www.xmission.com/~legalize/fractals/maxiter/index.html>
RSS feed: <http://www.xmission.com/~legalize/fractals/maxiter/maxiter-rss.xml>
Roger's blog is linked from the pages of rendered images. On his blog
he posts the GIF which have the parset embedded; I post 1600x1200 3x
antialiased JPEGs rendered from the parset.
The feed is catching up to the present and is currently grinding
through July images. Roger has been posting parsets that typically
take less time per image than the FOTD parsets and of course there are
far fewer parsets in the backlog to grind through, so this feed should
be caught up to the present in a short while.
Enjoy.
--
"The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download
<http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/>
Legalize Adulthood! <http://legalizeadulthood.wordpress.com>
FOTD -- September 19, 2010 (Rating 5)
Fractal visionaries and enthusiasts:
There *was* an antiquing trip on Saturday, which explains the
lateness and brevity of today's FOTD.
Today's image is named "Carnival Atmosphere". The excessively
gaudy colors inspired the name but also held the rating to a 5.
The scene is located in the same area of the same parent fractal
that held yesterday's image, though today's scene lies well west
of the northern large minibrot, in the East Valley area of a
smaller minibrot.
The parameter file calculation time of just under 2-1/2 minutes
is well within reason.
The image may also be seen on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
without the need for parameter-file calculation.
Near perfect conditions prevailed here at Fractal Central on
Saturday, with full sun and a temperature of 75F 24C. The
fractal cats, who were alone most of the day, shrugged it off as
just another routine day.
The next FOTD will most likely be posted on schedule. Until
then, take care, and do it again.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
CarnivalAtmosphere { ; time=0:02:28.24-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident
center-mag=-1.78282152665/+0.023995738155/8.6e+007\
/1/160/0 params=2.003/0/-0.00941066196782/0 float=y
maxiter=3600 inside=0 logmap=241
colors=000p59p26j3Ae3E`4IW4MR4PL5TG5XB6`66d16g38i5\
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zzLzzKzzJzzIzzHzzrzzszzszzszztzztzztzzuzzuzzuzzvzz\
wzztzzrzzozzmzzjzzhzzezzc }
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=========================================
Tendrils and the green of chlorophyll- that's veggieness. A Kerry Mitchell formula.
Fractint gif and re-sampled jpg at http://maxitersfractalfollies.blogspot.com.
In this case a re-sampling was almost mandatory, without anti-aliasing the
graphic is a dotted mess.
fract425.gif { ; blank
; blank
; calctime 0:02:18.03
; created Sep 18, 2010
; Fractint Version 2004 Patchlevel 9
reset=2004 type=formula formulafile=*.frm formulaname=field4_jul
passes=1
center-mag=+0.10863579474342960/+0.86293823038397370/64.10256
params=0.375/0.375/20000000/15 float=y maxiter=1500 inside=0
decomp=256 periodicity=0
colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\
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}
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
.
this bio is dated 2006:
http://departments.fmarion.edu/mathematics/museum/author.html
and
"Mr. Carlson currently lives and works in Fort Collins, Colorado. "
right up the road from me - maybe I stop by and say hello!
I remember the MBF program many years ago - I played with it for a while, still have it somewhere in my archives ...
I think he just retired and hanging out in "one of the best cities to live and retire in the USA" as Ft Collins is known.
I always thought he had been abducted by a UFO ....
.
FOTD -- September 18, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
Today's image lies in virtually the same parent fractal that
held the image of September 16. I say virtually the same
fractal because I have refined the real(p2) parameter so that
the parent fractal now has perfect X-axis symmetry rather than
almost perfect symmetry. The refinement makes no difference in
the surface appearance of the parent, but it gives a more satis-
factory base to today's image, (whatever that means). The scene
of today's fractal lies in a spurious valley of the large mini-
brot on the northern of the two main spikes of the parent.
The image rates only a 6. The colors lack a certain harmony
that could raise it to a rating of 7 or 8. And the sharply
angular shapes themselves have a vaguely threatening appearance.
The name "Caught in Flight" was the first thing that came to
mind when I stopped trying to think of a name. It has no
rational connection to the image.
The calculation time of 10-3/4 minutes is a bit long for today's
image. I suggest a trip to the FOTD web site at:
<http://www.Nahee.com/FOTD/>
to view the finished image.
The rain ended Thursday night, but dark lumpy clouds hung on all
day Friday here at Fractal Central. The temperature of 64F 18C
felt a bit chilly, though it was not all that unpleasant. The
fractal cats spent the day checking for unwanted stray cats in
the vicinity.
My day was appropriately busy for a Friday. With the garden
well watered, FL took it easy. Unless an unexpected antiquing
trip comes up on Saturday, the next FOTD will be posted in 24
hours. Until whenever, take care, and take it easy.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Caught_in_Flight { ; time=0:10:45.37-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident inside=0
center-mag=-1.751081846385343/+0.0208545867075613/\
2.07e+011/1/70/0 params=2.003/0/-0.00941066196782/0
float=y maxiter=12500 logmap=1111 mathtolerance=0/1
colors=000KZmKZmKZlKZkK_jK`iKahKbgKcfKdeLedMfcNgbO\
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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=========================================
A spiral with spirals. When I say fractal I say self-similarity. Fractint compatible gif
and re-sampled jpg at http://maxitersfractalfollies.blogspot.com.
fract420.gif { ; spirals
; blank
; calctime 0:09:55.07
; created Sep 16, 2010
; Fractint Version 2004 Patchlevel 9
reset=2004 type=formula formulafile=kerrym.frm
formulaname=bubbleboth_jul center-mag=0.135169/0.511853/13.33333
params=0.375/0.375/64/0.5/1/1 float=y maxiter=3600 inside=0
outside=atan periodicity=0
colors=05FOT_PT_PT`QU`QUaRVaRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYa\
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}
frm:bubbleboth_jul { ; copy
; Kerry Mitchell
; color Julia sets with small bubbles
; filled with swirls (combination of rays and circles)
;
; use outside=iter, decomp=256
; p1 = Julia parameter
; real(p2) = bailout (at least 4)
; imag(p2) = radius of bubble (try ~ .1)
; real(p3) = amount of circles (0 for only rays, try 0.5)
; imag(p3) = amount of rays (0 for only circles, try 0.5)
; zc is the variable used for iteration, z for coloring
;
zc=pixel, c=p1, maxr=real(p2), minr=imag(p2), scale=2*pi/minr
minset=0, iter=1, rzc=cabs(zc), minzc=zc
weight=real(p3)+imag(p3)
weightc=real(p3)/weight, weightr=imag(p3)/weight
;
; initial check: see if pixel magnitude falls within threshold
; if so, set minset flag, update minimum to current magnitude
;
if (rzc<minr)
minr=rzc, minzc=zc, minset=1
end if
:
iter=iter+1, zc=sqr(zc)+c, rzc=cabs(zc)
;
; iteration check: see if iterate falls within threshold
; if so, set minset flag, update minimum to current magnitude
;
if (rzc<minr)
minr=rzc, minzc=zc, minset=1
end if
;
; bailout
; set "iteration done" flag (iter=-1)
; scale minr to find decomp angle for circles
; take polar angle from minzc to ray decomp angle
; final angle is weighted average of ray and circle angles
; if a new minimum was never set (minset=0),
; set z=0 (color 0 under decomp)
;
if ((rzc>maxr)||(iter==maxit))
iter=-1
anglec=scale*minr, angler=imag(log(minzc))
angle=weightc*anglec+weightr*angler
z=(cos(angle)+flip(sin(angle)))*minset
end if
iter > 0
}
Roger Alexander
FOTD -- September 17, 2010 (No Rating)
Fractal visionaries and enthusiasts:
Today's image is another quick one from the Mandelbrot set. It
lies on the northeast shore line of the main bay, in the basin
of a very minor bud.
I named the image "A Fractal's Baby". After all, a minibrot
actually is a baby Mandelbrot set.
I could not give the image a rating. The Mandelbrot set is far
too familiar and well explored to supply many truly new images.
Perhaps the best point of the image is its lightning fast
calculation time of 2 seconds, which means little effort will
have been wasted if the image proves deficient.
All anxiety may be eliminated however by viewing the finished
image on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
The great weather of Wednesday here at Fractal Weather vanished
on Thursday, when we had an all-day rain with a temperature of
61F 16C. The fractal cats paid no attention to the outdoor
conditions. They were more interested in being fed.
My day was not too busy, but I spent too much time wheel-
spinning. FL watched with satisfaction as the rain watered her
flowers. The next FOTD will be posted in 24 hours. Until then,
take care, and be enlightened with the right enlightenment.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
A_Fractal's_Baby { ; time=0:00:02.03-SF5 on P4-2000
reset=2004 type=mandel center-mag=+0.3715633565073\
265/+0.2730086394944079/3.25e+013/1/-5/0 params=0/0
float=y maxiter=6000 bailout=9 inside=0 logmap=224
periodicity=6 mathtolerance=0.05/1
colors=000bjddjcejbfjahj`ij`jj_kkZmlYomXqnWsnVuoUw\
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jSzoQztOzyMztKzpIzlPzoVzr }
END PARAMETER FILE=========================================
