XaoS tutorial

This is a brief introduction to the basic XaoS features.

How to zoom

The main advantage of XaoS is that after a few seconds' delay to calculate the first image, you may choose any point with the mouse and press the left button. The image will start to zoom smoothly into the point you choose. You may move the mouse and zoom smoothly into interesting areas. By pressing the middle button (or left+right buttons) you may also move the image using “drag & drop” if you missed an interesting place. Unzooming is also possible by using the right button, but it is much slower because optimizations are not so effective as for zooming.

In case you think that the default speed is boring (it is quite slow, to make XaoS smooth on a slow computer) you may change it by pressing arrow up/down. But faster zooming is more expensive, so if the speed is too high you will see little but funny colorful blinking rectangles.


To make XaoS yet more impressive we made a special autopilot that automatically drives into interesting boundaries of the set. So you can press A, play your favorite music, drink coffee and relax. I never tried this but it should be really relaxing! 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.

Various fractal formulae

XaoS also supports formulae other than the Mandelbrot set. You may change formula using the number keys or SHIFT+letters.

On keys 1 to 5 are Mandelbrot sets of various power. The “normal” Mandelbrot set is on key 1.

On key 6 is a fractal called Newton. It is Newton's famous formula for finding roots.

On key 7 is the fourth ordered Newton fractal.

On key 8 is a fractal called Barnsley.

On key 9 is Barnsley's second fractal.

On key 0 is Barnsley's third fractal.

With keys SHIFT-A you can display a fractal called octo. It is a fractal that Thomas discovered in fractint.

With keys SHIFT-B you can display a fractal called Phoenix. It is a very nice and quite famous fractal.

With keys SHIFT-C you can display a fractal called Magnet. This fractal has quite a complex formula so it is a bit slow.

With keys SHIFT-D you can display the Magnet2 fractal.

The rest of the built-in fractals are accessible through an other menu, but you can still use the hotkeys.

On SHIFT-E is a fractal called Triceratops found by Arpad.

On SHIFT-F is a fractal called Catseye found by Arpad. This is more interesting if you change the bailout value.

On SHIFT-G is a fractal called Mandelbar. It was in Gnofract4d, and they found it at: http://mathworld.wolfram.com/MandelbarSet.html

On SHIFT-H is the Lambda fractal.

On SHIFT-I and SHIFT-J are the Manowar and Spider fractals, they were found by users of fractint. (Scott Taylor or Lee Skinner) It was on http://spanky.triumf.ca/www/fractint/ taylor_skinner_type.html

The next 3 fractals are famous classic fractals.

On SHIFT-K is the Sierpinski Gasket. You can change its shape by selecting another Julia seed. (This is for technical reasons.)

On SHIFT-L is the Sierpinski Carpet. It's shape can also be changed by selecting another Julia seed.

On SHIFT-M is the Koch Snowflake.

Out-coloring modes

To make fractals yet more interesting, more 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 key 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

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.

Like the coloring modes, planes have cryptic names. You guessed it, they're mathematical formulae. Here mu means coordinates in the normal complex plane. If you have coordinates in 1/mu plane, and you need coordinates in the a complex plane (to calculate the Mandelbrot set) you simply use the coordinates as mu. Lambda is another plane that can be converted to mu using a similar formula.

  • mu

normal mode.

  • 1/mu

Inversion: infinity goes to 0 and 0 goes to infinity.

  • 1/(mu+0.25)

Similar to inversion, but moves the center outside of the Mandelbrot set so that it looks parabolic.

  • lambda

Lambda plane.

  • 1/lambda

Inversion of lambda plane.

  • 1/lambda-1

Inversion with moved center.

  • 1/(mu-1.40115)

A very interesting mode for the Mandelbrot set. It makes small things

big, so you can browse the set's details easily.

Mandelbrot/Julia switching

Most of the fractals displayed by XaoS (currently all of them) 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 set 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 get back press M again. Some fractals (Barnsley and phoenix) are already in their Julia versions, because the Mandelbrot ones 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 preview mode

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.


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. Many of them look ugly, so press P again to get another one until you find one you like.


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.

Palette cycling

This is a very old trick that makes the Mandelbrot set a little flashier. You may enable or disable it using Y. In the truecolor modes you need to enable the palette emulator filter first. This is done via the E key, or from the filter menu.

Changing number of iterations

To calculate fractals perfectly, you need an infinite number of iterations. XaoS does just the first few of them, so after lots of zooming you may get into a place that looks quite boring, and the boundaries of the set are rounded, without any interesting details. This can be changed by changing the number of iterations:

Press and hold arrow right and wait until iterations are high enough. This may slow down calculation much. To reduce number of iterations press arrow left.

Changing resolution

XaoS usually starts in a low resolution (320×200 or thereabouts) to make calculations faster. If you have a fast computer or you need to save bigger .gif images, you may change the resolution. This can be done by pressing = in the full screen drivers, or simply by resizing the XaoS window.

Changing driver

XaoS usually has more than one driver available. You may change it on the fly in case you want a different one. For example, XaoS started in X11 can be switched at runtime to use the AA driver. This can be done from the UI menu.

This action is bit dangerous, because XaoS can crash during initialization if there is some problem with initialization; XaoS tries to initialize a new driver, and if it fails it attempts to return back to the original. Sometimes this is impossible, and all XaoS can do is terminate..

Other features

XaoS has many other features, but they don't fit into this tutorial. Most of them are available from the menu, so you can experiment with them. You might also want to see the animated tutorials from the help menu, to have an idea what XaoS can do.