path: root/catalogs/english.cat

# Message catalog file required to replay XaoS tutorials in
# English language
#
# Copyright (C) 1997 by Jan Hubicka
#
# Corrected by Tim Goowin
# Further corrections by David Meleedy
# And some more by Nix
#
# There are a few things you should know if you want to change or
# translate this file.
#
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#########################################################
#For file dimension.xaf

fmath "The math behind fractals"
fmath1 "Fractals are a very new field
of math, so there are still lots
of unsolved questions."
fmath2 "Even the definitions are not clean"
fmath3 "We usually call something a fractal 
if some self-similarity can be found"


def1 "One of the possible definitions is..."
#Definition from the intro.xaf is displayed here.
#If it is a problem in your langage catalog, let me
#know and I will create a special key
def2 "What does this mean?"
def3 "To explain it we first need
to understand what the topological and
Hausdorff Besicovich dimensions are."

topo1 "The topological dimension
is the \"normal\" dimension."
topo2 "A point has 0 dimensions"
topo3 "A line has 1"
topo4 "A surface has 2, etc..."

hb1 "The definition of the
Hausdorff Besicovich dimension
comes from the simple fact that:"
hb2 "A line that is zoomed so that it doubles
in length is twice as long as it was."
hb3 "On the other hand, the size
of a square that is similarly zoomed
grows by four times."
hb4 "Similar rules work in higher
dimensions too."
hb5 "To calculate dimensions from
this fact, you can use the
following equation:"
hb6 "dimension = log s / log z
where z is the zoom change and
s is the size change"
hb7 "for a line with zoom 2,
the size change is also 2.
log 2 / log 2 = 1"
hb8 "for a square with zoom 2,
the size change is 4.
log 4 / log 2 = 2"
hb9 "So this definition gives
the same results for normal shapes"
hb10 "Things will become more interesting
with fractals..."

hb11 "Consider a snowflake curve"
hb12 "which is created by repeatedly
splitting a line into four lines."
hb13 "The new lines are 1/3 the size of
the original line"
hb14 "After zooming 3 times, these lines will
become exactly as big as the
original lines."
hb15 "Because of the self similarity created
by the infinite repeating
of this metamorphosis,"
hb15b "each of these parts will
become an exact copy of the original
fractal."
hb16 "Because there are four such copies, the
fractal size grows by 4X"
hb17 "After putting these values in equations:
log 4 / log 3 = 1.261"
hb18 "We get a value greater than 1
(The topological dimension
of the curve)"
hb19 "The Hausdorff Besicovich dimension
(1.261) is greater than the
topological dimension."
hb20 "According to this definition, 
the snowflake is a fractal."

defe1 "This definition, however, is not
perfect since it excludes lots of
shapes which are fractals."
defe2 "But it shows one of the
interesting properties of fractals,"
defe3 "and it is quite popular."
defe4 "The Hausdorff Besicovich dimension
is also often called a 
\"fractal dimension\""

#########################################################
#For file escape.xaf
escape "The math behind fractals

chapter 2 - Escape time fractals"
escape1 "Some fractals (like snowflake)
are created by simple subdivision
and repetition."
escape2 "XaoS can generate a different
category of fractals - called
escape time fractals."
escape3 "The method to generate them
is somewhat different, but is also
based on using iteration."
escape4 "They treat the whole screen as
a complex plane"
escape5 "The real axis is placed horizontally"
escape6 "and the imaginary is placed vertically"
escape7 "Each point has its own orbit"
escape8 "The trajectory of which is calculated
using the iterative function, f(z,c)
where z is the previous position and c
is the new position on the screen."
escape9 "For example in the Mandelbrot
set, the iterative function is z=z^c+c"
orbit1 "In case we want to examine
point 0 - 0.6i"
orbit2 "We assign this parameter to c"
orbit3 "Iteration of the orbit
starts at z=0+0i"
orbit3b "Then we repeatedly calculate
the iterative function, and we
repeatedly get a new z value for
the next iteration."
orbit4 "We define the point that belongs to the
set, in case the orbit stays finite."
orbit5 "In this case it does..."
orbit6 "So this point is inside the set."
orbit7 "In other cases it would
go quickly to infinity."
orbit8 "(for example, the value 10+0i
The first iteration is 110, 
the second 12110 etc..)"
orbit9 "So such points are outside the set."

bail1 "We are still speaking about
infinite numbers and iterations
of infinite numbers..."
bail2 "But computers are
finite, so they can't
calculate fractals exactly."
bail3 "It can be proved that in the
case where the orbit's distance from
zero is more than 2, the orbit
always goes to inifinity."
bail4 "So we can interrupt calculations
after the orbit fails this test.
(This is called the bailout test)"
bail5 "In cases where we calculate points
outside the set, we now need just a
finite number of iterations."
bail6 "This also creates the colorful
stripes around the set."
bail7 "They are colored according to the
number of iterations of orbits needed
to fall in the bailout set."
iter1 "Inside the set we still
need infinite numbers of calculations"
iter2 "The only way to do it is to interrupt
the calculations after a given
number of iterations and
use the approximate results"
iter3 "The maximal number of iterations
therefore specifies how exact 
the approximation will be."
iter4 "Without any iterations you would create
just a circle with a radius of 2
(because of the bailout condition)"
iter5 "Greater numbers of iterations makes
more exact approximations, but
it takes much longer to calculate."
limit1 "XaoS, by default, calculates
170 iterations."
limit2 "In some areas you could zoom for a
long time without reaching this limit."
limit3 "In other areas you get
inexact results quite soon."
limit4 "Images get quite boring
when this happens."
limit5 "But after increasing the number
of iterations, you will get lots of new
and exciting details."
ofracts1 "Other fractals in XaoS are
calculated using different formulae
and bailout tests, but the method
is basically the same."
ofracts2 "So many calculations are required
that XaoS performs lots of
optimizations.

You might want to read about
these in the file
doc/xaos.info"

#########################################################
#For file anim.xaf
anim "XaoS features overview

Animations and position files"

#########################################################
#For file anim.xhf

anim2 "As you have probably noticed,
XaoS is able to replay animations
and tutorials."

anim3 "They can be recorded directly
from XaoS,"

languag1 "since animations and
position files are stored
in a simple command language"

languag2 "(position files are
just one frame animations)."

languag3 "Animations can be manually
edited later to achieve more
professional results."

languag4 "Most animations in these tutorials
were written completely manually,
starting from just a position file."

modif1 "A simple modification"

modif2 "generates an \"unzoom\" movie,"
modif3 "and this modification, a \"zoom\" movie."

newanim "You can also write completely
new animations and effects."

examples "XaoS also comes with
many example files, that can
be loaded randomly from the
save / load menu."

examples2 "You can also use position
files to exchange coordinates with
other programs."

examples3 "The only limits are your
imagination, and the command
language described in xaos.info."

#########################################################
#For file barnsley.xaf

intro4 "An introduction to fractals

Chapter 5-Barnsley's formula"

barnsley1 "Another formula
introduced by Michael Barnsley"

barnsley2 "generates this strange fractal."

barnsley3 "It is not very interesting
to explore,"

barnsley4 "but it has beautiful Julias!"

barnsley5 "It is interesting because it has
a \"crystalline\" structure,"

barnsley6 "rather than the \"organic\"
structure found in many other
fractals."

barnsley7 "Michael Barnsley has also introduced
other formulas."

barnsley8 "One of them generates this fractal."

#########################################################
#For file filter.xaf

filter "XaoS features overview

filters"

#########################################################
#For file filter.xhf

filter1 "A filter is an effect applied
to each frame after the fractal
is calculated."

filter2 "XaoS implements the
following filters:"

motblur "motion blur,"

edge "two edge detection filters,"

edge2 "(the first makes wide lines and is
useful at high resolutions,"

edge3 "the second makes
narrower lines),"

star "a simple star-field filter,"

interlace "an interlace filter, (this speeds up
calculations and gives the effect of
motion blur at higher resolutions),"

stereo "a random dot
stereogram filter,"

stereo2 "(if you are unable to see anything
in the next images and you can
normally see random dot stereograms,
you probably have the screen size
incorrectly configured---use `xaos
-help' for more information),"

emboss1 "an emboss filter,"  #NEW

palettef1 "a palette emulator filter, 
(enables color cycling on
truecolor displays)"	#NEW

truecolorf "a true color filter, (creates
true-color images on 8bpp displays)."

#########################################################
#For file fractal.xaf

end "The end."

fcopyright "The introduction to fractals
was done by Jan Hubicka in July 1997
and later modified and updated
for new versions of XaoS

Corrections by:
Tim Goodwin <tgoodwin@cygnus.co.uk>
and
David Meleedy <dmm@skepsis.com>
and
Nix <nix@esperi.demon.co.uk>"
# Add your copyright here if you are translating/correcting this file

suggestions "
Please send all ideas,
suggestion, thanks, flames
and bug-reports to:

xaos-discuss@lists.sourceforge.net

Thank You"

#########################################################
#For file incolor.xaf

incolor1 "Usually, points inside the set are
displayed using a single solid
color."

incolor2 "This makes the set boundaries
very visible, but the areas inside the
set are quite boring."

incolor3 "To make it a bit more
interesting, you can use the
value of the last orbit to assign
color to points inside the set."

incolor4 "XaoS has ten different
ways to do that. They are called
\"in coloring modes\"."

zmag "zmag

Color is calculated from
the magnitude of the last orbit."

#########################################################
#For file innew.xaf

innew1 "Decomposition like

This works in same way
as color decomposition
in outside coloring modes
"

innew2 "Real / Imag

Color is calculated from the
real part of the last orbit divided
by the imaginary part."

innew3 "The next 6 coloring modes are
formulas mostly chosen at random, or
copied from other programs."

#########################################################
#For file intro.xaf

fractal "...Fractals..."
fractal1 "What is a fractal?"

fractal2 "Benoit Mandelbrot's definition:
a fractal is a set for which the
Hausdorff Besicovich dimension
strictly exceeds the
topological dimension."

fractal3 "Still in the dark?"

fractal4 "Don't worry.
This definition is only important if
you're a mathematician."

fractal5 "In English,
a fractal is a shape"

fractal6 "that is built from pieces"

fractal7 "each of which is approximately a
reduced size copy of the whole
fractal."

fractal8 "This process repeats itself"

fractal9 "to build the complete fractal."

facts "There are many surprising
facts about fractals:"

fact1 "Fractals are independent of scale,"
fact2 "they are self similar,"
fact3 "and they often resemble objects
found in the nature"
#fact4 "such as clouds, mountains,
#or coastlines."
fact5 "There are also many
mathematical structures
that define fractals,"
fact6 "like the one you see on the screen."
fmath4 "Most fractals are
created by an iterative process"
fmath5 "for example the fractal known
as the von Koch curve"
fmath6 "is created by changing
one line"
fmath7 "into four lines"
fmath8 "This is the first
iteration of the process"
fmath9 "Then we repeat this change"
fmath10 "after 2 iterations..."
fmath11 "after 3 iterations..."
fmath12 "after 4 iterations.."
fmath13 "and after an infinite number of
iterations we get a fractal."
fmath14 "Its shape looks like one third of
a snowflake."
tree1 "Lots of other shapes could
be constructed by similar methods."
tree2 "For example by changing a line
in a different way"
tree3 "We can get a tree."
nstr "Iterations can possibly
introduce random noise into a fractal"
nstr2 "By changing a line into two"
nstr3 "lines and adding some small error"
nstr4 "you can get fractals looking like
a coastline."
nstr5 "A similar process could
create clouds, mountains, and lots of
other shapes from nature"

#######################################################
## mset.xaf

fact7 "Undoubtedly the most famous fractal is.."

mset "The Mandelbrot Set"
mset1 "It is generated from
a very simple formula,"
mset2 "but it is one of the
most beautiful fractals."
mset3 "Since the Mandelbrot set is a fractal,"
mset4 "its boundaries contain"
mset5 "miniature copies of
the whole set."
mset6 "This is the largest one, about 50
times smaller than the entire set."
mset7 "The Mandelbrot set is
not completely self similar,"
mset8 "so each miniature
copy is different."
mset9 "This one is about 76,000 times
smaller than the whole."
mset10 "Copies in different parts
of the set differ more."

nat "The boundaries don't just contain
copies of the whole set,"
nat1 "but a truly infinite variety
of different shapes."
nat2 "Some of them are surprisingly
similar to those found in nature:"
nat3 "you can see trees,"
nat4 "rivers with lakes,"
nat5 "galaxies,"
nat6 "and waterfalls."
nat7 "The Mandelbrot set also contains many
completely novel shapes."

###############################################################################
############

juliach "An introduction to fractals

Chapter 2-Julia"

julia "The Mandelbrot set is not the only
fractal generated by the formula:
z=z^2+c"
julia1 "The other is..."
julia2 "the Julia set"
julia3 "There is not just one Julia set,"
julia4 "but an infinite
variety of them."
julia5 "Each is constructed from a \"seed\","
julia6 "which is a point selected 
from the Mandelbrot set."
julia7 "The Mandelbrot set can be seen
as a map of various Julia sets."
julia8 "Points inside the Mandelbrot set
correspond to Julias with large
connected black areas,"
julia9 "whereas points outside the Mandelbrot set
correspond to disconnected Julias."
julia10 "The most interesting Julias have
their seed just at the boundaries of
the Mandelbrot set."

theme "The theme of a Julia set also
depends heavily on the seed point
you choose."
theme1 "When you zoom in
to the Mandelbrot set, you will get
a very thematically similar fractal"
theme2 "when switching to the
corresponding Julia."
theme3 "But zoom out again, and you discover"
theme4 "that you are in a completely
different fractal."
theme5 "Julia sets may seem to be quite
boring since they don't change themes"
theme6 "and remain faithful to the
seed chosen from the Mandelbrot set."
theme7 "But by carefully choosing the
seed point you can generate"
theme8 "beautiful images."

#########################################################
#For file keys.xhf

keys "Keys:

q          - stop replay              
Space      - skip frame               
             (can take a while)       
Left/Right - adjust speed of subtitles"

#########################################################
#For file magnet.xaf

intro7 "An introduction to fractals

Chapter 8-Magnet"

magnet "This is NOT the Mandelbrot set."
magnet1 "This fractal is called \"magnet\"
since its formula comes
from theoretical physics."
magnet2 "It is derived from the study
of theoretical lattices in the
context of magnetic renormalization
transformations."

similiar "Its similarity to the Mandelbrot set
is interesting since this is a real
world formula."

magjulia "Its julia sets are quite unusual."

magnet3 "There is also a second magnet fractal."

#########################################################
#For file new.xaf

new "What's new in version 3.0?"
speed "1. Speedups"
speed1 "The main calculation loops
are now unrolled and
do periodicity checking."
speed2 "New images are calculated using
boundary detection,"
speed3 "so calculating new images
is now much faster."
speed4 "For example, calculation
of the Mandelbrot set at
1,000,000 iterations..."
speed5 "calculating..."
speed6 "finished."
speed7 "XaoS has a heuristic that
automatically disables periodicity
checking when it doesn't expect the
calculated point to be inside the set
(when all surrounding points aren't)."
speed8 "Also the main zooming routines
have been optimized so zooming is
approximately twice as fast."
speed9 "XaoS now reaches 130FPS
on my 130Mhz Pentium."

new2 "2. Filters."
new3 "3. Nine out-coloring modes."
new4 "4. New in-coloring modes."
new5 "5. True-color coloring modes."
new6 "6. Animation save/replay."
newend "And many other enhancements, such
as image rotation, better palette
generation...  See the ChangeLog for
a complete list of changes." #NEW

#########################################################
#For file newton.xaf

intro3 "An introduction to fractals

Chapter 4-Newton's method"
newton "This fractal is generated by
a completely different formula:"
newton1 "Newton's numerical method for finding
the roots of a polynomial x^3=1."
newton2 "It counts the number of iterations
required to get the approximate root."
newton3 "You can see the three roots
as blue circles."
newton4 "The most interesting parts are in places
where the starting point is almost
equidistant from two or three roots."
newton5 "This fractal is very self similar
and not very interesting to explore."
newton6 "But XaoS is able to
generate \"Julia-like\" sets,"
newton7 "where it uses the error in the
approximation as the seed."
newton8 "This makes the Newton fractal
more interesting."
newton9 "XaoS can also generate an other
Newton fractal."
newton10 "Newton's numerical method for finding
the roots of a polynomial x^4=1."
newton11 "You can see the four roots
as blue circles."

#########################################################
#For file octo.xaf
intro6 "An introduction to fractals

Chapter 7-Octo"
octo "Octo is a less well known fractal."
octo1 "We've chosen it for XaoS
because of its unusual shape."
octo2 "XaoS is also able
to generate \"Julia-like\" sets,
similar to those in the Newton set."

#########################################################
#For file outcolor.xaf

outcolor "Out coloring modes"
outcolor1 "The Mandelbrot set is just
the boring black lake
in the middle of screen"
outcolor2 "The colorful stripes
around it are the boundaries
of the set."
outcolor3 "Normally the coloring is
based on the number of iterations
required to reach the bail-out value."
outcolor4 "But there are other
ways to do the coloring."
outcolor5 "XaoS calls them
out-coloring modes."

iterreal "iter+real

This mode colors the boundaries by
adding the real part of the last
orbit to the number of iterations."
iterreal1 "You can use it to make
quite boring images more interesting."

iterimag "iter+imag is similar to iter+real."
iterimag2 "The only difference is that it uses
the imaginary part of the last
orbit."

iprdi "iter+real/imag

This mode colors the boundaries by
adding the number of iterations to
the real part of the last orbit
divided by the imaginary part."

sum "iter+real+imag+real/imag

is the sum of all the previous coloring
modes."

decomp "binary decomposition

When the imaginary part is greater
than zero, this mode uses the number
of iterations; otherwise it uses the
maximal number of iterations minus
the number of iterations of binary
decomposition."

bio "biomorphs

This coloring mode is so called since
it makes some fractals look like
one celled animals."

#########################################################
#For file outnew.xhf

potential "potential

This coloring mode looks
very good in true-color
for unzoomed images."

cdecom "color decomposition"
cdecom2 "In this mode, the color is calculated
from the angle of the last orbit."
cdecom3 "It is similar to
binary decomposition but
interpolates colors smoothly."
cdecom4 "For the Newton type, it can be used
to color the set based on which root
is found, rather than the number of
iterations."

smooth "smooth

Smooth coloring mode tries to remove
stripes caused by iterations and
make smooth gradations."
smooth1 "It does not work for the Newton set
and magnet formulae since they have
finite attractors."
smooth2 "And it only works for true color and
high color display modes. So if you
have 8bpp, you will need to enable
the true color filter."

#########################################################
#For file outnew.xhf

intro5 "An introduction to fractals

Chapter 6-Phoenix"

phoenix "This is the Mandelbrot set for
a formula known as Phoenix."

phoenix1 "It looks different than the other
fractals in XaoS, but some similarity
to the Mandelbrot set can be found:"

phoenix2 "the Phoenix set also contains a
\"tail\" with miniature copies of
the whole set,"

phoenix3 "there is still a correspondence of
\"theme\" between the Mandelbrot
version and the Julias,"

phoenix4 "but the Julias are very different."

#########################################################
#For file plane.xaf

plane1 "Usually, the real part of a point
in the complex plane is mapped to
the x coordinate on the screen; the
imaginary part is mapped to the y
coordinate."

plane2 "XaoS provides 6 alternative
mapping modes"
plane3 "1/mu

This is an inversion - areas from
infinity come to 0 and 0 is mapped
to infinity. This lets you see what
happens to a fractal when it is
infinitely unzoomed."
plane4 "This is a normal Mandelbrot..."
plane5 "and this is an inverted one."
plane6 "As you can see, the set was
in the center and now it is
all around. The infinitely large
blue area around the set
is mapped into the small
circle around 0."
plane7 "The next few images will be
shown in normal, and then inverted mode
to let you see what happens"

plane8 "1/mu+0.25

This is another inverted mode, but
with a different center of inversion.
"
plane9 "Since the center of inversion lies
at the boundary of Mandelbrot set,
you can now see infinite parabolic
boundaries."
plane10 "It has an interesting effect on
other fractals too, since it usually
breaks their symmetry."

lambda "The lambda plane provides a
completely different view."

ilambda "1/lambda

This is a combination of
inversion and the lambda plane."

imlambda "1/(lambda-1)

This is combination of lambda,
move, and inversion."

imlambda2 "It gives a very interesting
deformation of the Mandelbrot set."

mick "1/(mu-1.40115)

This again, is inversion with a moved
center.  The center is now placed
into Feigenbaum points - points
where the Mandelbrot set is self
similar. This highly magnifies the
details around this point."

#########################################################
#For file power.xaf

intro2 "An introduction to fractals

Chapter 3-Higher power Mandelbrot sets"

power "z^2+c is not the only
formula that generates fractals."
power2 "Just a slightly modified one: x^3+c
generates a similar fractal."
power3 "And it is, of course, also
full of copies of the main set."

power4 "Similar fractals can be generated
by slightly modified formulae"

pjulia "and each has a corresponding series
of Julia sets too."

#########################################################
#For file truecolor.xaf

truecolor "True-color coloring modes"
truecolor1 "Usually fractals are colored using
a palette. In true-color mode, the
palette is emulated."
truecolor2 "The only difference is that the
palette is bigger and colors are
smoothly interpolated in coloring
modes."
truecolor3 "True-color coloring mode
uses a completely different
technique. It uses various parameters
from the calculation"
truecolor4 "to generate an exact
color - not just an index
into the palette."
truecolor5 "This makes it possible to display up
to four values in each pixel."
truecolor6 "True color coloring mode of course
requires true color. So on 8bpp
displays, you need to enable the
true-color filter."

#########################################################
#for file pert.xaf  #NEW (up to end of file)

pert0 "Perturbation"
pert1 "Just as the Julia formula uses
different seeds to generate
various Julias from one formula,"
pert2 "you can change the perturbation
value for the Mandelbrot sets."
pert3 "It changes the starting position of
the orbit from the default value of 0."
pert4 "Its value doesn't affect the
resulting fractal as much as the seed
does for the Julias, but it is useful
when you want to make a fractal more
random."

##########################################################
#for file palette.xaf

pal "Random palettes"
pal0 "XaoS doesn't come with large
library of predefined palettes
like many other programs, but
generates random palettes."
pal1 "So you can simply keep pressing 'P'
until XaoS generates a palette that
you like for your fractal."
pal2 "Three different algorithms
are used:"
pal3 "The first makes stripes going from
some color to black."
pal4 "The second makes stripes from black
to some color to white."
pal5 "The third is inspired by cubist
paintings."

###########################################################
#for file other.xaf

auto1 "Autopilot"
auto2 "If you are lazy, you
can enable autopilot to
let XaoS explore a fractal
automatically."
fastjulia1 "Fast Julia browsing mode"
fastjulia2 "This mode lets you morph
the Julia set according to the
current seed."
fastjulia3 "It is also useful as a preview of an
area before you zoom in - because of
the thematic correspondence between
the Julia and the point you choose,
you can see the approximate theme
around a point before you zoom in."
rotation "Image rotation"
cycling "Color cycling"
bailout "Bailout"
bailout1 "That's the Mandelbrot set with an
outcoloring mode 'smooth.'"
bailout2 "By increasing bailout to 64, you get
more balanced color transitions."
bailout3 "For most fractal types different bailout
values result in similar fractals."
bailout4 "That's not true for Barnsley fractals."




##############################################
#for file trice.xaf

trice1 "Triceratops and Catseye fractals"
trice2 "If you change the bailout value"
trice3 "of an escape-time fractal"
trice4 "to a smaller value,"
trice5 "you will get an other fractal."
trice6 "With this method we can get"
trice7 "very interesting patterns"
trice8 "with separate areas of one color."
trice9 "The Triceratops fractal"
trice10 "is also made with this method."
trice11 "Many similar pictures can be"
trice12 "made of Triceratops."
trice13 "The Catseye fractal"
trice14 "is like an eye of a cat."
trice15 "But if we raise the bailout value..."
trice16 "...we get a more interesting fractal..."
trice17 "...with bubbles..."
trice18 "...and beautiful Julias."

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#for file fourfr.xaf

fourfr1 "Mandelbar, Lambda, Manowar and Spider"
fourfr2 "This is the Mandelbar set."
fourfr3 "It's formula is: z = (conj(z))^2 + c"
fourfr4 "Some of its Julias are interesting."
fourfr5 "But let's see other fractals now."
fourfr6 "The Lambda fractal has a structure"
fourfr7 "similar to Mandelbrot's."
fourfr8 "It's like the Mandelbrot set
on the lambda plane."
fourfr9 "But Lambda is a Julia set,
here is MandelLambda."
fourfr10 "...fast Julia mode..."
fourfr11 "This is the fractal Manowar."
fourfr12 "It was found by a user of Fractint."
fourfr13 "It has Julias similar to the whole set."
fourfr14 "This fractal is called Spider."
fourfr15 "It was found by a user of Fractint, too."
fourfr16 "And it has Julias similar
to the whole set, too."

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#for file classic.xaf

classic1 "Sierpinski Gasket, S.Carpet,
Koch Snowflake"
classic2 "This is the famous
Sierpinski Gasket fractal."
classic3 "And this is
the escape-time variant of it."
classic4 "You can change its shape by selecting"
classic5 "another 'Julia seed'"
classic6 "This fractal is the Sierpinski Carpet."
classic7 "And here is it's escape-time variant."
classic8 "This is famous, too."
classic9 "And finally, this is
the escape-time variant"
classic10 "of the Koch Snowflake."

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#for file otherfr.xaf

otherfr1 "Other fractal types in XaoS"