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XaoS is a realtime interactive fractal zoomer. This means that it lets you zoom smoothly into any place in the fractal you choose without the long calculation required by most other fractal generators. It has many other features too, like different fractal types, autopilot, special coloring modes, random palette generation, color cycling, etc.
You can use the mouse to zoom in and out. The pan function allows you to drag and drop the image in any direction to change the center without zooming in or out. The button you press determines the action performed:
| Action | Mouse Button | Mac Equivalent |
|---|---|---|
| Zoom in | Left |
Click |
| Zoom out | Right |
Ctrl+Click |
| Pan |
Center or Left+Right
|
Shift+Click |
Zooming in and out also works with the mouse wheel.
On Macs with a single button mouse, use the Mac equivalents to simulate the other buttons.
Note: The behavior of the mouse buttons can change when special modes are enabled. If you enable rotation, the first button is used to rotate the image. Also, in fast Julia mode, the first button is used to change the seed.
Many XaoS functions have keyboard shortcuts available.
XaoS has many built-in animated tutorials that will teach you about Fractals and demonstrate many of its features. These tutorials are accessible through the Help menu. For each tutorial, you can watch the whole story, or skip to the part you're interested in.
XaoS has a special autopilot that automatically drives into interesting
boundaries of the set. So you can press a, play your favorite music, have a drink,
and relax. Many pictures in the XaoS gallery were discovered using the autopilot.
The autopilot also has some additional features. It turns back when the zoomed picture stops being interesting, and is able to spot when it's zoomed into a really boring part (or has reached the limit of floating point numbers) and restart zooming from the top.
In order to get the most out of XaoS, you need to understand a few things about how fractals are calculated.
Different mathematical formulas yield very different fractals. XaoS supports many
formulae other than the Mandelbrot set. These formulas can be selected from the
Fractal > Formula menus. You may also change formula using number keys 0-9
or SHIFT+letters.
Most of the fractals displayed by XaoS have two forms: Mandelbrot and Julia. Every point in a Mandelbrot set has its own Julia set. To see more about this correspondence, try the tutorial on Julia sets from the Introduction to fractals.
In the Mandelbrot mode, you can get a corresponding Julia by moving the mouse
to an interesting point and pressing m. To switch back press m again. Some
fractals (Barnsley and Phoenix) are already in their Julia versions, because
the Mandelbrot forms are boring. But by pressing m in such fractal you should
get the Mandelbrot version, and by choosing another point as the base point and
pressing M again you should get a completely different fractal. The most
interesting points for Julia sets are at the boundaries of the Mandelbrot set.
Most of the Julias inside or outside the set are boring.
Fast Julia mode is a quick way to find a point to use as a base for the Julia
set.. Just press j and a small Julia set will be displayed in the top left
corner. Then move the mouse around with button 1 depressed, and the Julia for
the point the mouse is over will be automatically generated.
Fractals are calculated by looping over a formula repeatedly. The behavior of the
formula after a certain number of iterations determines the colors of the fractal.
As you dive deeper into the fractal, the number of iterations required increases.
In order to complete the calculations in a reasonable amount of time, XaoS uses an
iteration limit. If you start to see areas of low detail on the interior of a fractal,
you probably need to increase the iteration limit. Be aware that selecting a higher
iteration limit will slow down the calculation of the fractal. The iteration limit
can be entered directly from the menu or decreased and increased
using the arrow keys Left and Right, respectively.
Computers calculate floating point numbers with a limited precision. Usually on Intel processors, XaoS uses 80-bit precision. After a few minutes of zooming in, the fractal will stop zooming and become blocky as the precision of your CPU reaches its limit. If you reach this point, there is no way around it except to zoom back out and choose a different area. Don't worry, there are still plenty of interesting areas to explore since you will already have zoomed in approximately 64,051,194,700,380,384 times. Algorithms with unlimited precision exist, but they are too slow for real-time zooming.
You can increase or decrease the zooming speed using the Up and Down arrow
keys. Zooming faster means your computer has less time to calculate the fractal, so
the image may get blocky if your CPU can't keep up. If this happens, stop zooming
for a while, and the details will fill in again. Zooming out is generally slower
To make fractals more interesting, different coloring modes for points outside
the set are provided. "Classical coloring mode" uses the number of iterations
that the orbit required to escape to (nearly) infinity. You can change this
mode from the Fractal menu or by pressing c To see more about coloring
modes, try the tutorial on Incoloring modes from the XaoS features overview.
Those cryptic names for coloring modes are mathematical formulae, where iter means number of iterations, real means real coordinate of last orbit, and imag means imaginary coordinate of last orbit.
In-coloring mode is similar to out-coloring, except that it changes how things
inside the set are displayed. This can also be changed from the Fractal
menu or by pressing f.
You might also want to see the tutorial on Out-coloring modes from the XaoS features overview.
All fractals displayed by XaoS are functions with a complex parameter. It can
be displayed in the normal complex plane, where x is the real part of the
number, and y is the imaginary part; but it can also be displayed in a number
of other planes. You can select the plane to use from the Fractal menu, or
by pressing i.
If you think that the default XaoS colors are ugly or you are just bored by
them you can change it by pressing p. XaoS will automatically generate random
palettes. Some of them look ugly, so press p again to get another one until you
find one you like.
This is a very old trick that makes the Mandelbrot set a little flashier. You
may enable or disable it using Y. Usually, you need to enable the palette emulator
filter first. This is done via the e key, or from the Filter menu.
Many interesting effects are done by post-calculation filters.
XaoS has filters that do everything from embossing, through motion-blurring,
right through to turning the fractal into a stereogram. To enable them use the
Filter menu or press e.