XAOS TUTORIAL
This is text version of tutorial. For html one (with images) see
http://www.paru.cas.cz/~hubicka/XaoS
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Why use XaoS
We decided to make XaoS, because all fractal browsers we know needs
long time to calculate every image. You may browse nice images
generated by them but real impression from fractal - they self
similarity and possible infinite zooming into nice part of fractals
can be seen only in animation. There are many programs available that
makes nice animations but they takes long time to calculate and lots
of space on disc. Most of animations are quite ugly because their
authors can't see it without many hours of calculations. I found
special algorithm that saves up to 99.98% of calculations during
zooming. I am not first, who discovered it. Later I found some demos,
that makes real-time zooming but I don't know any that is interactive
and as fast as XaoS. XaoS is able to generate full-screen 320x200
animation on 486 in reasonable speed (5-20 frames per second). It uses
several methods to save calculation - Uses pixel from previous image,
solid guessing, symmetry, avoids calculation inside Mandelbrot set and
much more.
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How to zoom
Main advantage of XaoS is that after few seconds needed to calculate
first image you may choose some point by mouse and press left button.
Image will start to zoom smoothly into point you choose. You may move
mouse and zoom smoothly into interesting areas. By pressing middle
button (or left+right) you may also move image using "drag & drop" in
case you missed some interesting place. UN-zooming is also possible by
right button, but it is much slower because optimizations are not so
effective as for zooming.
By pressing button here: After six seconds of zooming: XaoS at startup
XaoS after zooming To make this animation XaoS calculated more than
25*6 frames of 320*200 pixels. Every pixel needs aprox 60 iterations.
So by normal algorithm you need: 25*6*620*200*60 = 576000000
iterations! Suppose that every iteration on some computer with
Mandelbrot coprocessor needs one instruction. On 66MHz it needs 8
seconds to calculate it!
In case you think that default speed is boring (it is quite slow to
make XaoS smooth on slow computer) you may change it by pressing arrow
up/down. But understand that faster zooming is more expensive so if
speed is too high you should see just funny colorfull blinking
rectangles.
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Autopilot
To make XaoS yet more impressive we did special autopilot that
automatically drives into interesting boundaries of set. So you should
press 'A', play your favorite music, drink coffee and relax. I never
tried this but it should be really relaxing! Many pictures in XaoS
gallery are discovered using autopilot.
Autopilot has also some additional features. It return back in case
zoomed picture is not interesting anymore. Also is able to detect,
when zoomed into really boring part or reached limit of floating point
numbers and restart zooming.
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Various fractal formulas
XaoS also supports other formulas than Mandelbrot set. You may change
formula using keys '1' - '0'.
On keys '1' - '5' are Mandelbrot sets with various power. The "normal"
Mandelbrot set is: z=z^2+c on key '1'. For example on key '3' is
z=z^4+c.
On key '6' is fractal called octo. It is some fractal that Thomas
discovered in fractint. Looks nice in other planes..see bellow.
On key '7' is Newton. It is famous newton formula for finding roots.
On key '8' is Bernsley. It is another formula comming from real
world.. I forgot what means.
On key '9' is Phoenix. It is very nice and quite famous fractal.
On key '0' is Magnet. This fractal has quite complex formula so it is
bit slow.
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In-coloring modes
To make fractal yet more interesting more coloring modes for points
outside set are provided. "Classical coloring mode" uses number of
iterations that orbit required to escape boundaries. After pressing
'C' following menu is displayed:
Please select outcoloring mode:
1 - iter
2 - iter+real
3 - iter+imag
4 - iter+real/imag
5 - iter+real+imag+real/imag
6 - binary decomposition
7 - biomorphs
Now you may choose mode by pressing key '1' - '7'
Those crtyptic names are mathematical formulas where iter means number
of iterations, Real real coordinate of last orbit, Imag imaginary
coordinate of last orbit.
iter
this is classical coloring mode that takes number of iterations
iter+real
this mode takes number of iterations and adds real part of last
position of orbit
iter+imag
similar to previous one except takes imaginary part
iter+real/imag
as previous but adds real part divided by imaginary part. There
is no mathematical reason for it. Just looks well..
iter+real+imag+real/imag
this is summary of all previous modes..
binary decomposition
takes number of iterations in case that imaginary part is
greater than zero. Otherwise takes maximal number of iterations
minus number of iterations
biomorphs
takes number of iterations in case that imaginary or real part
is inside boundaries. Otherwise takes maximal number of
iterations minus number of iterations
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In-coloring mode
Similiar to out coloring mode is in coloring. It is only way how to
display thinks inside set. Only one mode is provided. Takes color by
magnitude of Z. It can be enabled by pressing 'F'. Press of again to
disable it.
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Planes
All fractals displayed by XaoS are function with complex parameter. It
can be displayed in normal complex plane where x is real part of
number and y is imaginary. But may be also displayed in some other
planes. After pressing 'I' following menu is displayed:
Please select display plane:
1 - mu
2 - 1/mu
3 - 1/(mu+0.25)
4 - lambda
5 - 1/lambda
6 - 1/(lambda-1)
7 - 1/(mu-1.40115)
Another cryptic names. And, you guessed, another mathematical
formulas. Here mu means coordinates in normal complex plane. In case
you have coordinates in 1/mu plane and you need complex plane (to
calculate mandelbrot) you simply use coordinates as variable mu.
Lambda is another plane that can be converted to mu using similiar
formula.
mu
normal mode..
1/mu
Inversion-infinity is in 0 and 0 is in infinity.
1/(mu+0.25)
Similar to inversion but moves center outside of Mandelbrot so
it looks parabolic
lambda
lambda plane
1/lambda
Inversion of lambda plane
1/lambda-1
Inversion with moved center
1/(mu-1.40115)
Very interesting mode for Mandelbrot set. Makes small thinks
big. So you can browse its details.
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Mandelbrot/julia switching
Most of fractals displayed by XaoS (currently all of them) have two
forms: Mandelbrot and Julia. Every point in Mandelbrot form has its
own Julia set. You may display it moving mouse to point you selected
and pressing 'M' . To return back press 'M' again. Some fractals
(barnsley and phoenix) are already in their Julia versions, because
Mandelbrot ones are boring. But by pressing 'M' in such fractal you
should get to Mandelbrot version and by choosing another point as base
and pressing 'M' again you should get completely different fractal.
The most interesting points for Julia sets are at boundaries of
Mandelbrot set. Most of Julia inside or outside set are boring. By
pressing 'M' here: You will get following Julia: XaoS at startup Julia
version
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Fast julia preview mode
New to 2.2 releasi is Fast julia preview mode. It is sollution for
question: What point use as base for julia set. Just press 'J' and
small julia set will be displayed at top left corner. Then move mouse
arround with pressed button 1 and julia to corresponding point will be
automatically generated. Note that this function works just for
Mandelbrot power 2-6, barnsley and partially magnet fractal. Also
output isn't perfect especially with magnet fractal differs from real
one. Fast preview mode
Fast mode
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Palette changing
In case you think that default XaoS colors are ugly or you are just
bored by them you may try to change it by pressing 'P'. XaoS will
generate automatically random palette. Many of them looks ugly so
press 'P' again to get different one.
UNIX/X11 specific note:
In 8bpp pseudo-color X11 colors can look very ugly, because palette is
shared with other programs and when XaoS can't allocate its palette it
simply uses simpler one. Also changing of colors takes long time. To
avoid this use true-color or hi-color displays, close some colorful
applications like netscape, or use -private switch. Using -private
speeds up palette changing or rotation, because recalculation of
mandelbrot after every change is not required.
Different mandelbrot
Changed palette.
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Palette cycling
This is very old trick that makes mandelbrot set more interesting. You
may enable/disable it using 'Y'.
This trick is easy to implement on clasical PC VGA cards. At other
platforms this should be implemented by other way than normal palette
changing, pecause palette is shared with other programs(X windows in
pseudocolor) or truecolor display does not have palette at all. XaoS
emulates this feature at most such platforms but this emulation should
slow down a much. For example at truecolor or text displays this
requires redrawing of whole screen Some drivers does not support it at
all.
And at X11 with 8bpp pseudocolor palette rotation does not work in
default shared palette mode. You need to use -private switch to enable
this feature.
When palette rotation is enabled, you may control its speed using key
left and right. Normally this keys are used for changing number of
iterations. See following part.
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Changing number of iterations
To calculate fractals perfectly you need infinite number of
iterations. XaoS does just first few of them so after longer zooming
you may get into place that looks quite boring and boundaries of set
are rounded w/o any interesting details. This should be changed by
changing number of iterations:
Press and hold arrow left and wait until iterations are high enough.
This may slow down calculation much..to reduce number of iterations
press arrow right.
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Random dot stereograms
Fractal images are also good as base for random dot stereogram. In
case you don't know what this mean, please point your browser to
altavista or other searching engine and find some article about this
images because browsing such images is not easy. They makes possible
to generate three dimensional images at normal monitor without any
additional hardware.
To enable this mode press 'E'. XaoS is also able to generate this
images in animation so you may use all normal XaoS functions except
palette changing/rotation, because this is unnecesary. To make
animation yet more exciting XaoS emulates "falling" into the set. So
during zooming distance from set is getting lower and lower. But never
lets you fall down so when set reeaches level of your monitor distance
is changed again and you are far away.
To make this in real sizes xaos needs to know exact sizes of your
monitor. Because most platforms does not know this values you need to
use command line options to tune this. Otherwise you should have
problems with seeing anything in images generated by XaoS (in case
your monitor is too big or resolution low). Or images are not as deep
as normaly (in case your monitor small or resolution high).
By default xaos expect my 15" monitor (29.0cm x 21.5 cm). Another
problem is virtual screen supported by some windowed enviroments(like
X11) that makes program think that resolution is higher and you see
just part of this screen. This cause problem with recalculation screen
size to pixel size.
The worst think you should do at all is to run fullscreen XaoS in some
graphical window(windows 95 or OS/2 ?) where XaoS don't know that real
size of his window is different.
Following command line options are provided for this.
-screenwidth
-screenheight
lets you specify size of your screen in centimeters. Note that
you need to specify size of image at you monitor. Not size with
some borders or such.
-pixelwidth
-pixelheight
lets you specify exact size of one pixel in cases I described
bellow.
This options are used by some other parts of XaoS too. So you should
use them even you don't want to see stereograms. You should write
small starting script that passes correct parameters.
Another problem should happend when window is smaller than 8cm. In
this case you will be unable to see anything.
So correct way to see XaoS stereogram is:
* start XaoS with options specifying corect size of screen or pixel
* Sit 60cm away from monitor
* Put your eyes to distance 8.5 cm from each other :)
* In case you use windowed enviroment resize XaoS window to make it
wider than, say, 15 cm.
* press 'E'
* concentrate far away from monitor(you should try to use your
reflection..) until random points will get into different
distances and you will see mandelbrot
* Curefully use you mouse to zoom into interesting areas(it is easy
to lose concentration when you are not trained. Or use autopilot.
* Enjoy animation :)
Last problem should be that fractal is deformed This can be caused by
wrong geometry of your monitor. Eye is extremly ensible for distances
so should see very small changes in geometry that are normally
unvisible.
Example
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Changing of resolution
XaoS usually starts in low resolution (320x200 or so) to make
calculations faster. In case you have fast computer or you need to
save bigger .gif images you may change resolution. This should be done
by pressing '=' in full screen drivers or simply by resizing XaoS
window.
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Changing of driver
XaoS usually have more than one driver available. You may change it on
the fly in case you want different one. For example XaoS started in X
windows and you want to use curses driver. This can be done by
pressing 'V'. This action is bit dangerous, because XaoS can crash
during inicialisation in case of some unexpected problem. Also
colormap is set to default one.
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Solid guessing
XaoS used solid guessing. This mean that when it wants to calculate
pixel but all pixels around are blue it simply expects that this pixel
is blue too. This speeds up a much but also may cause inexact results.
Especially after zooming when error is propagated.
Many fractals fans now asks why I don't use boundary detection. Please
see ahgorithm descriptions that explains why I decided for solid
guessing.
You may solve this problem by two ways:
* press 'R' to let XaoS recalculate image
* use 'G' to control solid guessing.
After pressing 'G' folliwing menu is displayed:
Plase select solid guessing mode
1 - solid guessing disabled
2 - guess maximally 2x2 rectangles
3 - guess maximally 3x3 rectangles
4 - guess maximally 4x4 rectangles
5 - guess maximally 5x5 rectangles
6 - guess maximally 6x6 rectangles
7 - guess maximally 7x7 rectangles
8 - guess maximally 8x8 rectangles
Now you may choose range. Default is 2x2. Larger range means faster
calculation and less exact results. By pressing '1' you may disable
this feature.
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Drawing options
Sometimes calculations takes so much time so framerate should fall
very very low. In this cases xaos automatically reduces details so
animation is still quite smooth. You may control This feature by
pressing 'T'. Following menu is displayed:
Plase select drawing mode
1 - fast drawing disabled
2 - use only during animation
3 - use also for new images
This lets you choose when such resolution lowering is possible. By
pressing '1' you may disable it at all. '2' is the default mode. '3'
enables this also for new images. So when XaoS recalulates screen nice
pixelizing effect is performed. Only disadvantage is that it is slower
than normal calculation.
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Status informations
After pressing '?' you may invoke displaying of status information. In
this list you may find all informations about current image. Example
status:
Fractal name:Mandelbrot
Fractal type:Mandelbrot
View:[-2.416666666667,-1.250000000000]
size:[3.333333333333,2.500000000000]
Screen size: 158:98
Iterations: 128 Palette size:248
Autopilot:Off Plane:mu
zoomspeed:8.000000
incoloring:iter outcoloring:iter
Parameter:noneiter
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Other functions
Image saving
By pressing 'S' you may save current image into interlaced gif
image. Fractal is recalculated before saving to get best
possible output
Interrupting of calculation
By pressing 'Z' you may interrupt current calculation in case
it is too long and you know that it is bad..
Displaying of current status
By pressing space during calculation you may invoke displaying
of current status. It looks bit strange because some part are
already calculated and some part are from some old image. But
you may guess how result will look like..
Online help
By pressing 'H' hyperuglytext viewer with help text is
displayed. Using keys '1' and '2' you may browse help.
Quit
This is really not necessary..but by 'Q' you may quit XaoS.
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Curses driver
Curses driver bit differs from normal drivers because it allows you to
display real-time zooming on text terminals. It has many advantage
over other drivers so I will quickly describe them.
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Online help
Online help briefly describing keys is also available by pressing 'H'.
Very significant part is at the end where is documentation specific to
your driver. It may contain some interesting informations not contaned
in documentations about XaoS at all.
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Command line options
as every good program XaoS also have command line options. Run xaos -h
for help, or see xaos.1 or xaosman.txt for more documentation.
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Interested in more informations?
You may subscribe to our discusion about XaoS at
majordomo@horac.ta.jcu.cz by sending message
Subscribe xaos
you may also subscribe xaos-announce in case you want to be informed
about new releases or xaos-devel in case you want to become XaoS
developer (and you will be welcomed)
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Send all comments, questions, suggestions, etc... to
Jan Hubicka, hubicka@limax.paru.cas.cz
Copyright © 1996 by Jan Hubicka. All rights reserved.
Last Modified: Fri Jul 26 14:09:01 CDT 1996
